Lines and Angles
Overview
Lines and Angles is a foundational geometry chapter for Class 7. It explores different types of lines, rays, and line segments, and the various angles formed when lines meet or are cut by a transversal. Students learn about complementary, supplementary, adjacent, and vertically opposite angles, and discover important properties of parallel lines cut by a transversal, building skills essential for higher geometry.
Typed Notes
Basic Terms: Lines, Rays, and Angles
A line extends infinitely in both directions. A ray starts at a point and goes infinitely in one direction. A line segment has two fixed endpoints. An angle is formed when two rays meet at a common point called the vertex. Angles are measured in degrees (°). Types of angles: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°), and reflex (between 180° and 360°). Understanding these basics is necessary before studying angle relationships.
Pairs of Angles: Complementary, Supplementary, Linear Pair, and Vertically Opposite
Complementary angles add up to 90°. For example, 35° and 55° are complementary. Supplementary angles add up to 180°. For example, 110° and 70° are supplementary. A linear pair consists of two adjacent angles whose non-common sides form a straight line; they always add up to 180°. Vertically opposite angles are formed when two lines intersect; the angles across from each other are equal. For example, if two lines cross and one angle is 65°, the angle directly opposite is also 65°.
Transversal and Parallel Lines
A transversal is a line that crosses two or more lines at distinct points. When a transversal cuts two parallel lines, it creates eight angles. Corresponding angles (same position at each intersection) are equal. Alternate interior angles (on opposite sides of the transversal, between the parallel lines) are equal. Co-interior angles, also called same-side interior or consecutive interior angles, are supplementary (add to 180°). These properties are used to find unknown angles and to prove that two lines are parallel in geometric problems.
Checking Parallelism Using Angle Properties
We can determine whether two lines are parallel by examining the angles formed with a transversal. If corresponding angles are equal, the lines are parallel. If alternate interior angles are equal, the lines are parallel. If co-interior angles add up to 180°, the lines are parallel. Conversely, if none of these conditions hold, the lines are not parallel. This reverse application of angle properties is very useful in proofs and constructions. Always identify the type of angle pair first before applying the correct rule.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01Complementary angles sum to 90°; supplementary angles sum to 180°.
- 02A linear pair is formed by two adjacent angles on a straight line and always sums to 180°.
- 03Vertically opposite angles are formed at the intersection of two lines and are always equal.
- 04When a transversal cuts two parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-interior (same-side interior) angles are supplementary.
- 05Two lines are parallel if a transversal makes equal corresponding or alternate interior angles with them.
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Two angles are complementary. One angle measures 34°. Find the other angle.
Two lines intersect and one of the angles formed is 112°. Find all four angles.
A transversal cuts two parallel lines. One of the alternate interior angles is 73°. Find the other alternate interior angle.
Two supplementary angles are in the ratio 2:3. Find both angles.
A transversal cuts two parallel lines. A co-interior angle is 65°. Find the other co-interior angle.
Lines and Angles covers basic geometric terms and important angle relationships. Key ideas include complementary (sum 90°) and supplementary (sum 180°) angles, linear pairs, and vertically opposite angles. When a transversal intersects parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-interior angles are supplementary. These properties help solve unknown angle problems and verify whether lines are parallel.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.Which pair of angles adds up to 90°?
Q2.Two lines intersect. One angle is 45°. What is the vertically opposite angle?
Q3.A transversal cuts two parallel lines. The corresponding angles are:
Q4.If one angle of a linear pair is 120°, what is the other angle?
Mark karo — dashboard par progress dikhega.