NCERT Class 9 Solutions: Quadrilaterals (Chapter 8) Exercise 8.2 – Part 4
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Corresponding Angles
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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.
Q7 ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse AB and parallel to BC intersects AC at D. Show that

D is the midpoint of AC


Solution:
Give triangle of ABC at C, a line through the midpoint M of hypotenuse AB and parallel to BC intersects AC at D.

In ,

M is the midpoint of AB and

Thus; D is the midpoint of AC (Converse of midpoint theorem)


(Corresponding angles)

Also,

Thus, and


In and ,

(D is the midpoint of side AC)

(Each 90°)

(Common)

Thus, by SideAngleSide congruence condition.

by Corresponding Part of Congruent Triangles

also, (M is midpoint of AB)

Hence,