# NCERT Class 9 Solutions: Quadrilaterals (Chapter 8) Exercise 8.2 – Part 4

• Corresponding Angles

• Corresponding Angle:-the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

Q-7 ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that

1. D is the mid-point of AC

Solution:

• Give triangle of ABC at C, a line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D.

1. In ,

• M is the midpoint of AB and

• Thus; D is the midpoint of AC (Converse of mid-point theorem)

2. (Corresponding angles)

• Also,

• Thus, and

3. In and ,

• (D is the midpoint of side AC)

• (Each 90°)

• (Common)

• Thus, by Side-Angle-Side congruence condition.

• by Corresponding Part of Congruent Triangles

• also, (M is mid-point of AB)

• Hence,

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