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

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 AB=AC. Show that

  1. AD bisects BC

  2. AD bisects A .

Solution:

Give isosceles triangle ABC AD is altitude and AB=AC

Give Isosceles Triangle ABC

Give isosceles triangle ABC AD is altitude and AB=AC

Given,

AD is an altitude of isosceles triangle ABC and AB=AC

  1. In ΔABD and ΔACD ,

    ADB=ADC=90° AB=AC (Given) AD=AD (Common)

    Therefore, ΔABDΔACD by RHS congruence condition.

    Now, BD=CD (by CPCT)Thus, AD bisects BC

  2. BAD=CAD (by Corresponding Parts of Congruent Triangles)Thus, AD bisects A.

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 ΔPQR (see Fig). Show that:

  1. ΔABMΔPQN

  2. ΔABCΔPQR

Give 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

Give Two Triangle Are ABC and PQR

Give 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 ΔPQR

AB=PQ,BC=QR and AM=PN

  1. 12BC=BM and 12QR=QN (AM and PN are medians)

    also, BC=QR12BC=12QRBM=QN

    In ΔABM and ΔPQN , AM=PN (Given) AB=PQ (Given) BM=QN (Proved above) Therefore, ΔABMΔPQN by SSS congruence condition.

  2. In ΔABC and ΔPQR , AB=PQ (Given) ABC=PQR (by Corresponding Parts of Congruent Triangles) BC=QR (Given)

    Therefore, ΔABCΔPQR by Side- Angle-Side congruence condition.

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