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

Triangle of ABC with right angle at C.

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.
Thus, (Corresponding Parts of Congruent Triangles)
(M is midpoint of AB)
Therefore,