NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 – Part 2

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Right Angle-Hypotenuse-Side (RHS)

Give two right triangle ABC and DEF ,BC=EF and AC=DF

Give Two Right Triangle ABC and DEF

Give two right triangle ABC and DEF ,BC=EF and AC=DF

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

  1. AD bisects BC

  2. AD bisects .

Solution:

Isosceles Triangle ABC

Isosceles triangle ABC AD is altitude and AB=AC

Given,

AD is an altitude of isosceles triangle ABC and

  1. In and ,

    (Given) (Common)

    Therefore, by RHS congruence condition.

    Now, (by CPCT)Thus, AD bisects BC

  2. (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:

Two Triangles Are ABC and PQR

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

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

  1. and (AM and PN are medians)

    also,

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

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

    Therefore, by Side- Angle-Side congruence condition.