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.

Inand , (Given) (by Corresponding Parts of Congruent Triangles) (Given)

Therefore, by Side- Angle-Side congruence condition.