# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 – Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Right Angle-Hypotenuse-Side (RHS)

**Theorem**: Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and the corresponding side of the other triangle.

Q-2 AD is an altitude of an isosceles triangle ABC in which Show that

- AD bisects BC
- AD bisects .

Solution:

Given,

AD is an altitude of isosceles triangle ABC and

- In and ,

(Given) (Common)

Therefore, by RHS congruence condition.

Now, (by CPCT) Thus, AD bisects BC

- (by Corresponding Parts of Congruent Triangles) Thus, AD bisects

Q-3 Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of (see Fig) . Show that:

Solution:

Given, Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of

and

- and (AM and PN are medians)

also,

In and , (Given) (Given) (Proved above) Therefore, by SSS congruence condition.

- In and , (Given) (by Corresponding Parts of Congruent Triangles) (Given)

Therefore, by Side- Angle-Side congruence condition.