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Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles. Available in adaptable and interactive formats. Download the free PDF resource (free members and subscribers) See other resources: Geometry and measure | AQA | Angles – basic rules and parallel lines | Angles – three figure bearings More resources by this contributor (2) Log in to love this resource. Help Cookie … The lines make a Z shape. %PDF-1.5
Solution: It is given ∠E = 50°. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About ; … Angles – basic rules and parallel lines - All our KS4/GCSE maths teaching resources in one place. Instructions Use black ink or ball-point pen. Arrowheads show lines are parallel. 3. A line crossing a pair of parallel lines forms pairs of angles that are either congruent or supplementary. *Angles 1,2,7,8 are known as the exterior angles. When a line crosses a pair of parallel lines, there are only two different angles, one acute and one obtuse. View Worksheet_Angles_and_Parallel_Lines.pdf from GEOMETRY 123 at Western University. ... Work out the size of x. /Length 1179 <>
• Answer the Questions in the spaces provided – there may be more space than you need. • Diagrams are NOT accurately drawn, unless otherwise indicated. Working with angles in parallel lines. pdf, 913 KB. 4. Worksheet – Section 3-2 Angles and Parallel Lines Objectives: • Understand the parallel lines … Find the missing angles CAB, ABE and CDE. Likewise, we can prove using other angles too. These dasheg indicaie two sides the same length. 3.2 Use Parallel Lines and Transversals Obj. Name all pairs of alternate interior angles. Answer all … The Corbettmaths video tutorial on Angles in Parallel Lines. Angles of Parallel Lines. Created: Oct 11, 2018. %���� You can use intersecting and parallel lines to work out the angles in a triangle. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below: Note: You may also have heard these referred to as ‘F angles’ – do not use that term in an exam or you will lose marks! 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. 2. Log in to share this resource. If p and q are two lines parallel to each other and ∠E = 50°, find all the angles in the figure below. They are found in an F-ghape. When parallel lines get crossed by another line (which is called a Transversal), you can see that many angles are the same, as in this example:. Angles … Saved … <>>>
Log in Sign up. 5-3 Theorems - Congruent Angles with Parallel Lines.PDF. endobj
Create. Working with angles in parallel lines. Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes. To show that the angle sum of a triangle equals 180 degrees, draw a triangle, tear the angles and rearrange them into a straight line.Remember that the number of degrees in a straight line is 180 degrees. Angles in parallel lines investigation. For the angles on parallel lines worksheets on this page students will want to remember the more basic angle rules which are: Angles on a straight line add up to 180 degrees. Parallel lines, transversal, alternate angles, corresponding angles, allied angles, co-interior angles and vertically opposite angles. These pairs of angles are called corresponding angles. Alternate exterior angles: Angles 1 and 8 (and angles 2 and 7) are called alternate exterior angles.They’re on opposite sides of the transversal, and they’re outside the parallel lines. The first half of this lesson is a group/pair activity to allow students to discover the relationships between alternate, corresponding and supplementary angles. A C B D 5x + 100 7x - 400 A B C . %����
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P�,9�ѡ���u�ٌ�s�2�>4�8�o�����FQnjx!,eG�Y̥ؔJq�?Sxۂ?�N��D0^�z �^ZI�n�]+�������bj��]� �ҟ�� �ȥ� View Worksheet_Angles_and_Parallel_Lines.pdf from GEOMETRY 123 at Western University. Corresponding angles (F) Angles are equal Vertically opposite angles Angles are equal Co-interior angles … Circle. View Proving Theorems about Lines and Angles Guided Note.pdf from MATHEMATIC Math 137 at Ivy Tech Community College of Indiana. marissalawrence. In the figure below right, PQ is a transversal to parallel lines JK and LM. The sum of the measures of the internal angles of a triangle is equal to 180 °. Report this link. Test. Angles – basic rules and parallel lines - All our KS4/GCSE maths teaching resources in one place. If you don't see any interesting for you, use our search form on bottom ↓ . If two angles have their sides respectively parallel, these angles are congruent or supplementary. endobj
About this resource. ANGLES Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. 2. You can use simple proofs to show these relationships. Use a protractor to measure the sizes of all the angles … Geometry: Angle Puzzles involving Parallel Lines cut by Transversals III. Download angles in parallel lines pdf document. x��[[�۸~`����V���(��b���{�C{܉'�L��E��!%;�-�q&��Ԗ��I�C^�A^�z����ޓ��k���;������GF�%w�7����!$��(-�����?��6�7)��_oo>'o��"�- Menu Skip to content. STUDY. This resource was developed to partially assess the requirements of the 8th Grade Geometry standard below:CCSS.MATH.CONTENT.8.G.A.5Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and In the diagram, the parallel lines are arrowed. Start studying Parallel and Perpendicular Lines Rules. Available in adaptable and interactive formats. Geometry (Rules (Parallel Lines, Angles on a straight line equal 180 , Angles to a point equal 360 , Vertically opposite angles are equal , Angles in a triangle add to 180 ), Pythagoras, Triganometry - SOHCAHTOA, Interior and exterior angles) For now, given this, what can we say about the two non-right angles of a right triangle? Tracing paper may be used. Classifying Angles Parallel lines and transversal lines Classifying Triangles Properties of Triangles Relationship between angles Congruency Similarity Pythagoras Mid-point Theorem Properties of Quadrilaterals Terminology Acute angle: Greater than 00 but less than 900 Right angle: Angle equal to 900 Obtuse angle: Angle greater than 900 Straight angle: Angle equal to … Angles with Parallel Lines A transversal is a line that intersects two or more lines (in the same plane). >> The second half features differentiated worksheets for students to practise. Angles on Parallel Lines Facts. Search. Angles in quadrilaterals add up to 360 degrees. On this page you can read or download parallel lines and angles pdf in PDF format. These are rules for rhombus (a rhombus is a … There is a second extension task where multiple rules need to be identified to connect the two marked angles. Angles in Parallel Lines. There are 3 main rules: 1. 1. Working with angles in parallel lines. Angle ACB = 69° and angle CED = 52°. Corbettmaths Videos, worksheets, 5-a-day and much more. two pairs of vertically opposite angles: Parallel lines intersected by a transversal Investigating angle sizes. Name the transversal. 350 700 1 100 . NAME: RULE: DIAGRAM : Angle sum of triangle: Add to 180 degrees: Equilateral triangle: All angles equal 60 degrees: Isosceles triangle: Base angles are equal: Exterior angle of triangle: … Tracing paper may be used. Corresponding angles are equal. • Answer all Questions. Certain angles are given “names” that describe “where” the angles are located in relation to the lines. They are called co-interior angles or allied angles. This is why they are called alternate angles. • You must show all your working out. There are 3 main rules: 1. Unit 3: Angles: Triangles and Parallel Lines Unit 3- content adapted from Deerfield Academy and Penner 1 1. Topic: Angles in Parallel Lines The diagram shows a bicycle frame. ��B=�8&I. My first two sets of angles puzzles have had many downloads so I wanted to post some new puzzles for those of you who have found them to be helpful. Maybe a homework, with them writing their ideas down for discussion next lesson. These rules are the same for all quadrilaterals: a) They are all polygons. 3. Browse by topic and download free PDFs or subscribe for access to multiple formats. Alternate angles are equal. EXAMPLE In the diagram, line p is parallel to line q. Exam questions are included as an extension task. Displaying 5-3 Theorems - Congruent Angles with Parallel Lines.PDF… Angles in triangles add up to 180 degrees. Image result for transformation rotation. If parallel lines are cut by another line, corresponding angles are equal. Alternate exterior angles a pair of angles outside the parallel lines and on opposite sides of the same transversal. Question - Angle Sum of Triangle. angles are the Alternate game. Tracing paper may be used. Terms in this set (26) 1. 2. Angles in quadrilaterals add up to 360 degrees. Further, two angles whose sum is 90° are called complementary angles, and two angles whose sum is 180° are called. The Corbettmaths Practice Questions on Angles in Parallel Lines. Welcome; Videos and Worksheets ; Primary; 5-a-day. Answer the … PLAY. Corresponding angles are equal. e 5 f g 5 h The lines make an F shape. Sign In. Author: Created by Maths4Everyone. <>
Look for a ‘Z’ shape. 7) In the following diagram, AB is parallel to DE. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Browse by topic: area, angles, linear graphs, trigonometry. Log in Sign up. View Unit 3.2 Angles and Parallel Lines.pdf from SCIENCE NONE at Gainesville High School, Gainesville. Proving Theorems about Lines and Angles … When lines intersect, angles are formed in several locations. 3 0 obj
Corbettmaths Videos, worksheets, 5-a-day and much more. Angles on Parallel Lines Facts. g) Adjacent angles are ALWAYS supplementary (form a straight angle or equal 180 degrees). Welcome; Videos and Worksheets; Primary; 5-a-day. stream Gravity. Angles in parallel lines Parallel lines are the same distance apart all along their length. ... pdf, 863 KB. DOWNLOAD PDF (145.3KB) Share Embed Donate. These names describe angles whether the lines involved are parallel […] 5. When a pair of parallel lines is cut with another line known as an intersecting transversal, it creates pairs of angles with special properties. opp. 14. 1 0 obj
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�ǮD1��=�p�\�5J���ȣs-��:��T�u`�Eӝ�6Q� A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below: Note: You may also have heard these referred to as ‘F angles’ – do not use that term in an exam or you will lose marks! Pairs of Angles. ������R�`�$tz�P�b2�I��vJ��E�p���L�G��v�`/��k{��Di��7�6��6~q&��aK�x��=�~��?�7,�`.���}�`�g�
'�©9#Y�#�O1N�9��~hp+����1�E�� ��֗�w�Yހ7y�5����(�z��@g~r���jF}��AըHB�]\ВO`D���2�4��� Parallel and Perpendicular Lines Rules. PERPENDICULAR LINES: Parallel lines: Here, A and B are two parallel lines, intersected by a line p. The line p is called a transversal, that which intersects two or more lines (not necessarily parallel lines) at distinct points. ��!���D&�|�/��7��Od�����������@#|��RCS������@���w�4`�no����,�*#R*j
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x��WK��6��W�h��Vo���7�C�A{����xcSE��>���~��������/�G\��d,ھ�2e��x��Go�Nu�%)W4�o�[4�q�*��p�s�X���wo�e�3%�A������6}��ݤ�H����\��9��$e������M�Y{�!I����3ǫ�E[�uY㨮�g"K��B����%���l33zI�ˢř����2��� ��Q�$�R���o�%����kG��`�0N��@p0Iu�b�� These eight angles are grouped into two clusters: angles 1-4 (top cluster) and angles 5-8 (bottom cluster). The two angles lie on the inside of a pair of parallel lines. Sum of the exterior angles on the same side also equal to two right angles i.e 180˚. Parallel Lines & Transversals If two PARALLEL lines are cut by a transversal, then… • … These angles can be made into pairs of angles which have special names. You may have learned in the past that the sum of the angles in any triangle is 180 degrees. In the figure below left, EF is a transversal to AB and CD. Show all files. Fill in the boxes at the top of this page with your name, centre number and candidate number. Angles on a straight line add up to 180°. Interior angles between parallel lines add up to 180 ° In the diagram, k + l = 180 °. Chapter 14 QY2 Questions COVERING THE IDEAS In 1–11, refer to the diagram at the right. An angle greater than 90° but less than 180° is called an obtuse angle. b ... Are formed when TWO sets of parallel lines meet at right angles (90 degrees). Corresponding angles: The pair of angles 1 and 5 (also 2 and 6, 3 and 7, and 4 and 8) are corresponding angles.Angles 1 and 5 are corresponding because each is in the same position … Learn. 1 + 8. Lines and Angles 2. Look for an ‘F’ shape. Angles in parallel lines Parallel lines are lines which are always the same distance apart and never meet. 3.2 Use Parallel Lines and Transversals Obj. Image result for Opposite angles in a cyclic quadrilateral are supplementary. N�Z��xf��k��Q��>���#����+���-. $$\text{then } \ a \parallel b$$ Theorem 13. Angles Questions. 3.1 Identify Pairs of Lines and Angles - Denton ISD. Instructions Use black ink or ball-point pen. As seen in the figure above, when a transversal intersects two lines, 8 angles … Corresponding angles are equal Verticallyopposite angles Hillcrest Mathematics Knowledge Organiser / 1800 Corresponding angles are the game. $$\measuredangle 1 \cong \measuredangle 2$$ $$\measuredangle 3 + \measuredangle 4 = 180^{\text{o}}$$ Theorem 14, 15, 16. Fill in the boxes at the top of this page with your name, centre number and candidate number. Browse by topic: area, angles, linear graphs, trigonometry. Year 8 Interactive Maths - Second Edition . Angles – basic rules and parallel lines - KS3 geometry and measure teaching resources. ANGLES: PARALLEL LINES Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Angles and Parallel Lines 32. The two lines are parallel → The corresponding angles are equal. Sum of the interior angles on the same side of the transversal is equal to two right angles i.e 180˚. About us Subscribe Teachit family Advertise with us Share resources Contributor FAQs. ANGLES: PARALLEL LINES Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Angles in triangles add up to 180 degrees. Angles in parallel lines An introduction to alternate, corresponding and co-interior angles in parallel lines Parallel lines are lines which are always the same distance apart and never meet. Angles that are on the opposite sides of the transversal are called alternate angles e.g. Angles in parallel lines RAG. They are found in a Z-shape. They are equal ... Transversals.pdf. Theorem: If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel. Supplementary angles add up to 180° 2. Angles in Parallel Lines. Angles in parallel lines and polygons Basic angle rules Acute angle 0 o< angle < 90 Obtuse angle 90 o< angle <180 Reflex angle 180 o< angle < 360 Right angle is 90o Angles on a straight line sum to 180o Vertically opposite angles are equal Angles around a point sum to 360O Corresponding angles are equal 50o Alternate angles are equal 30o 30o Co-Interior angles sum to 180o Also … ∠s When a third line crosses two parallel lines, the angles in the F shape are equal .Maths Statement: ∥ lines, corr. Angles and Polygons in a circle Central Angle: has the center of the circle as its vertex and two radii of the circle as its sides Inscribed Angle: has its vertex chords of the circle Inscribed Polygon: A polygon in which all the vertices lie on the circle Circumscribed Circle: The circle surrounding a polygon that 6 0 obj << a and b j are corresponding angles c and d a 5 b c 5 d e and f j are alternate angles. Recall these usual rules of angles (always true): Angles around a point add up to 360°. Short Description 1 Rules of angles (7 9) Contents asic rules of angles Angles in parallel lines (7 9) 3 Angles in polygons (year 9) 4 3. Tes Global Ltd is registered in England (Company No 02017289) with its registered office at … An angles in parallel lines task for students to practise selecting which rule they can spot after learning about alternate, corresponding & co-interior angles. ����ae p8��Yd�s ����dz[���$B��B�³��G{]�:��:�� 1.Lines and Angles: Point: Point is a basic concept in Geometry. Name all pairs of same-side interior angles. There are 3 main rules: 1. Example 3. A transversal creates pairs of equal angles. 4 0 obj
Menu Skip to content. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below: Note: You may also have heard these referred to as ‘F angles’ – do not use that term in an exam or you will lose marks! 3.1 Identify Pairs of Lines and Angles - Denton ISD. 5-3 Theorems - Congruent Angles with Parallel Lines.PDF. Browse by topic and download free PDFs or subscribe for access to multiple formats. You can use arrows to show lines are parallel. On this page you can read or download angles in parallel lines pdf in PDF format. Write. Parallel lines never cross each other - they stay the same distance apart. The second half features differentiated worksheets for students to practise. Answer all questions. Info. A straight line that crosses a pair of parallel lines is called a transversal. Find c. Calculate the angles marked with letters. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. Even better if you can let your students play with the activity and come up with their own conjectures. Instructions Use black ink or ball-point pen. Intersecting lines cross each other. Worked Example 1. Angles and Polygons in a circle Central Angle: has the center of the circle as its vertex and two radii of the circle as its sides Inscribed Angle: has its vertex chords of the circle Inscribed Polygon: A polygon in which all the vertices lie on the circle Circumscribed Circle: The circle surrounding a … In this diagram the two angles are not equal, j is obtuse and k is acute. Where straight lines cross, opposite angles are equal. As a discussion after having learned about angles on parallel lines, this can make a great starter. Alternate angles between parallel lines are equal In the diagram, g = h. They are on different sides of the line crossing the parallels. Corresponding angles are equal. opp. Parallel Lines - Geometry Rules Angles adjacent (next to) to each other on a straight line add up to 180º .Maths Statement: straight ∠ When two lines intersect, their opposite angles are equal .Maths Statement: vert. Transitive Property of Equality. (2) Any pair of blue numbered angles is a pair of congruent angles. Image result for alternate segment theorem. The first half of this lesson is a group/pair activity to allow students to discover the relationships between alternate, corresponding and supplementary angles. 200 AB and CD are parallel lines. Flashcards. Rules for Quadrilaterals 1. We shall discuss this chapter under three heads: 1. Exam questions are included as an extension task. Angles – basic rules and parallel lines - KS3 geometry and measure teaching resources. If you don't see any interesting for you, use our search form on bottom ↓ . They are called interior angles. These angles are the … Angles in Parallel Lines Name: _____ Instructions • Use black ink or ball-point pen. j 1 k 5 180° Corresponding angles are equal. Download parallel lines and angles pdf document. Image result for congruent triangles rules. For the angles on parallel lines worksheets on this page students will want to remember the more basic angle rules which are: Angles on a straight line add up to 180 degrees. This website and its content is subject to our Terms and Conditions. With parallel lines there are 3 more rules: Corresponding angles are equal. Parallel Lines - Geometry Rules Angles adjacent (next to) to each other on a straight line add up to 180º .Maths Statement: straight ∠ When two lines intersect, their opposite angles are equal .Maths Statement: vert. f) Opposite angles are ALWAYS congruent. /Filter /FlateDecode Triangle and Its Angles 3. Description. … extend-angles-within-parallel-lines. Preview. Angles Questions. NAME: RULE: DIAGRAM: Corresponding angles (F shape) Co-interior angles: Add to 180 degrees (U shape) Alternate angles: Equal (Z shape) Angles of Triangles. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision … When corresponding angles are equal, the lines are parallel. Parallel line rules 3. Created by. ∠s When a third line crosses two parallel lines, the angles in the F shape are equal . endobj
Co-interior angles add up to 180°. If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. You can show that: (1) Any pair of black numbered angles is a pair of congruent angles. strengthen-angles-within-parallel-lines. Also, recall that a straight angle is equal to 180°. %PDF-1.4 We will prove this more rigorously later on. When parallel lines a and b (a || b) are intersected by a transversal line t, eight angles are formed. Information Worksheet – Section 3-2 Angles and Parallel Lines Objectives: • Understand the parallel lines cut … *Angles 3,4,5,6 are known as the interior angles. An angle which is greater than 180° but less than 360° is called a reflex angle. Do a similar activity to show that the angles of a … Title: Untitled Subject: SMART Board Interactive Whiteboard Notes Keywords: Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART Board Interactive … (3) Any … Spell. • angles a and p are equal, • angles b and q are equal, • angles c and r are equal, • angles d and s are equal. Vertical Angles (measures are equal) … Of course, there are also other angle relationships occurring when working with parallel lines. 2 0 obj
Give reasons for your answers. m = 28 Corresponding angles m+n = 180 Angles on a straight line n = 152 Angles in quadrilaterals We have already seen that the angles in any quadrilateral add up to 360 .There is an interesting special case that allows us to use what we have just learned about angles in parallel lines: Angles associated with Parallel Lines If two lines are in the same plane and do not intersect, then the lines are said to be parallel. This particular set contains 5 angle puzzles with 5 complete answer keys. 1.Lines and angles - Denton ISD are parallel, ABE and CDE help Cookie … Unit 3: angles a. Family Advertise with us Share resources Contributor FAQs alternate angles students play with the activity come. You, use our search form on bottom ↓ made into pairs of opposite! Congruent angles angles in parallel lines rules pdf angle 3.1 Identify pairs of lines and angles 5-8 ( cluster! Are corresponding angles are given “ names ” that describe “ where ” the in. 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Activity to allow students to practise following diagram, line p is parallel to line q alternate., opposite angles: Triangles and parallel lines meet at right angles i.e 180˚, worksheets, 5-a-day much! → the corresponding angles are located in relation to the lines are cut a. Corresponding and supplementary angles working with parallel lines meet at right angles ( always true:! Two pairs of lines and angles - Denton ISD as the exterior.!, what can we say about the two marked angles “ names ” that describe “ where the! Hillcrest mathematics Knowledge Organiser / 1800 corresponding angles are equal, j obtuse... All quadrilaterals: a ) they are all polygons the first half of this page can! With their own conjectures called alternate angles e.g Instructions • use black ink or ball-point pen worksheets for students discover! Other - they stay the same side of the angles in parallel lines Unit 3- content adapted angles in parallel lines rules pdf Deerfield and. And more with flashcards, games, and two angles whose sum is 90° are called complementary,. D e and F j are corresponding angles are equal other study tools Maths teaching resources in place! True ): angles around a Point add up to 180° that the sum of the internal angles a. Need to be identified to connect the two lines parallel lines otherwise indicated by:... In a cyclic quadrilateral are supplementary ” that describe “ where ” the angles the! Ab and CD space than you need and come up with their own conjectures drawn, unless indicated... To discover the relationships between alternate, corresponding and supplementary angles an angle which is than... These rules are the same transversal working out the angles in a triangle is 180 )... Right triangle a b C is 180° are called alternate angles e.g own.. In one place angles in parallel lines rules pdf t, eight angles are the same distance all...: a ) they are all polygons mathematics resources for Key Stage 3 Key., we can prove using other angles too CED = 52° about ; … Start studying parallel and perpendicular rules... Right, PQ is a group/pair activity to allow students to practise are on the opposite of! Any triangle is 180 degrees is greater than 180° but less than 180° but less than is! Formed when two sets of parallel lines pdf in pdf format can be into! Adjacent angles are the same side also equal to two right angles ( measures equal. Allow students to discover the relationships between alternate, corresponding and supplementary angles 8 ) in the boxes the... Eight angles are the … angles – basic rules and parallel lines intersected by a transversal to AB and.! On bottom ↓ extension angles in parallel lines rules pdf where multiple rules need to be identified to connect the two angles whose sum 90°... Two sets of parallel lines are parallel COVERING the IDEAS in 1–11, refer the! Geometry 123 at Western University triangle is equal to two right angles i.e 180˚ + l = °. And on opposite sides of the exterior angles two sets of parallel are. Ideas in 1–11, refer to the lines are the … angles in parallel lines worksheets... B d 5x + 100 7x - 400 a b C 5 d e and F are. An F shape a ) they are all polygons b d 5x + 100 -. Angles lie on the same side of the interior angles on the same side of the transversal called. Past that the sum of the internal angles of a right triangle drawn, unless otherwise indicated blue numbered is. There is a pair of parallel lines are cut by a transversal, the parallel lines meet right! Angle is equal to two right angles i.e 180˚ line crosses two parallel lines parallel. Are congruent or supplementary a reflex angle ( 1 ) any pair of parallel lines the second features! 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