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 Equation Show that

  1. AD bisects BC

  2. AD bisects Equation .

Solution:

Angle β Angle β: Angle between C, D, C' Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [A, C] Segment g Segment g: Segment [A, C] Segment h Segment h: Segment [C, B] Segment h Segment h: Segment [C, B] Segment i Segment i: Segment [C, D] A text1 = "A" B text2 = "B" C text3 = "C" D text4 = "D"

Isosceles Triangle ABC

Isosceles triangle ABC AD is altitude and AB=AC

Given,

AD is an altitude of isosceles triangle ABC and Equation

  1. In Equation and Equation ,

    Equation Equation (Given) Equation (Common)

    Therefore, Equation by RHS congruence condition.

    Now, Equation (by CPCT)Thus, AD bisects BC

  2. Equation (by Corresponding Parts of Congruent Triangles)Thus, AD bisects Equation

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 Equation (see Fig). Show that:

  1. Equation

  2. Equation

Segment g Segment g: Segment [A, C] Segment g Segment g: Segment [A, C] Segment h Segment h: Segment [C, B] Segment g_1 Segment g_1: Segment [A_1, C_1] Segment g_1 Segment g_1: Segment [A_1, C_1] Segment h_1 Segment h_1: Segment [C_1, B_1] Segment f Segment f: Segment [A, D] Segment f Segment f: Segment [A, D] Segment f Segment f: Segment [A, D] Segment f Segment f: Segment [A, D] Segment i Segment i: Segment [D, B] Segment j Segment j: Segment [A_1, E] Segment j Segment j: Segment [A_1, E] Segment j Segment j: Segment [A_1, E] Segment j Segment j: Segment [A_1, E] Segment k Segment k: Segment [E, B_1] Segment l Segment l: Segment [C, D] Segment l Segment l: Segment [C, D] Segment l Segment l: Segment [C, D] Segment m Segment m: Segment [C_1, E] Segment m Segment m: Segment [C_1, E] Segment m Segment m: Segment [C_1, E] A text1 = "A" B text2 = "B" C text3 = "C" P text4 = "P" Q text5 = "Q" R text6 = "R" M text7 = "M" N text8 = "N"

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 Equation

Equation and Equation

  1. Equation and Equation (AM and PN are medians)

    also, Equation

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

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

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

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