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Understanding Lines and Angles for Class VII: Parallel, Perpendicular, and More

This guide, prepared by Pranab Ranjan Sahu and guided by Mr. Jitendra Nayak, TGT (Mathematics) at JNV, Deogarh, Odisha, focuses on essential concepts of lines and angles for Class VII students. It covers definitions and examples of parallel lines, perpendicular lines, along with transversal lines. The guide explains various types of angles such as vertical, supplementary, corresponding, alternate interior, alternate exterior, and consecutive interior angles, providing illustrations and methods to find missing angle measures.

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Understanding Lines and Angles for Class VII: Parallel, Perpendicular, and More

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  1. PREPARED BY PRANAB RANJAN SAHU & GROUP Class VII LINES AND ANGLES GUIDED BY MR. JITENDRA NAYAK TGT(MATHEMATICS) JNV, Deogarh, Odisha

  2. B A D l C m PARALLEL LINES • Def: line that do not intersect. • Illustration: • Notation:l || mAB|| CD

  3. Examples of Parallel Lines • Hardwood Floor • Opposite sides of windows, desks, etc. • Parking slots in parking lot • Parallel Parking

  4. m n PERPENDICULAR LINES • Def: Lines that intersect to form a right angle. • Illustration: • Notation:m n • Key Fact: 4 right angles are formed.

  5. Ex. of Perpendicular Lines • Window panes • Streets: Belmont and Cicero

  6. 30 Transversal • Def: a line that intersects two lines at different points • Illustration: t

  7. Vertical Angles • Two angles that are opposite angles. t • 14 • 2  3 • 5  8 • 6  7 1 2 4 3 6 5 7 8

  8. Vertical Angles • Find the measures of the missing angles t 125  ? 125  55  ? 55 

  9. t 1 2 4 3 6 5 7 8 Supplementary Angles/Linear Pair • Two angles that form a line (sum=180) • 1+2=180 • 2+4=180 • 4+3=180 • 3+1=180 • 5+6=180 • 6+8=180 • 8+7=180 • 7+5=180

  10. Supplementary Angles/Linear Pair • Find the measures of the missing angles t ? 108  72  180 - 72 ? 108 

  11. 1 2 3 4 5 6 7 8 Corresponding Angles • Two angles that occupy corresponding positions. t • 15 • 2  6 • 3  7 • 4  8 Top Left Top Right Bottom Left Bottom Right Top Left Top Right Bottom Left Bottom Right

  12. Corresponding Angles • Find the measures of the missing angles t 145  35  ? 145 

  13. 30 Alternate Interior Angles • Two angles that lie between parallel lines on opposite sides of the transversal t • 3  6 • 4  5 1 2 3 4 5 6 7 8

  14. Alternate InteriorAngles • Find the measures of the missing angles t 82  82  98  ?

  15. Alternate Exterior Angles • Two angles that lie outside parallel lines on opposite sides of the transversal t • 2  7 • 1  8 1 2 3 4 5 6 7 8

  16. Alternate ExteriorAngles • Find the measures of the missing angles t 120  ? 120  60 

  17. 30 Consecutive Interior Angles • Two angles that lie between parallel lines on the same sides of the transversal t • 3 +5 = 180 • 4 +6 = 180 1 2 3 4 5 6 7 8

  18. Consecutive InteriorAngles • Find the measures of the missing angles t 180 - 135 135  45  ?

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