# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.1 – Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Co-interior angles

When two lines are cut by a third line (transversal) **co**-interior angles are between the pair of lines on the same side of the transversal. If the lines are parallel the co-interior angles are supplementary (add up to 180 degrees) .

Q-7 AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that and (see Fig) . Show that

Solution:

Given, P is mid-point of AB.

- (Adding both sides)

In , (P is mid-point of AB) (Given) Therefore, (By Angle-Side-Angle congruence condition.

- (By corresponding Part of Congruent Triangles) .

Q-8 In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see Fig) . Show that:

- ΔAMC ≅ ΔBMD
- ∠ DBC is a right angle.
- ΔDBC ≅ ΔACB
- CM = 1/2 AB

Solution:

Given, right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to point D

M is the mid-point of AB and

- In and (M is the mid-point) (Vertically opposite angles) (Given)

Therefore, (By Side-Angle-Side congruence condition) .

- (By Corresponding Parts of Congruent Triangles) Therefore, as alternate interior angles are equal. Now, (co-interiors angles)
- In ΔDBC and ΔACB, (Common) (Right angles) (By Corresponding Parts of Congruent Triangles, already proved)

Therefore (By Side-Angle-Side congruence condition)

- (M is mid-point)