RD Sharma Class 9 Solutions Chapter 10 Exercise 10.4 (Updated for 2024)

RD Sharma Class 9 Solutions Chapter 10 Exercise 10.4: Here at Kopykitab we believe in achieving good grades by providing the best guides for Class 9 Maths. Here are RD Sharma’s solutions for Class 9 Maths for the same purpose. You can see how subject matter experts have made the solutions explanatory and easy to understand. You can download the RD Sharma Class 9 Solutions Chapter 10 Exercise 10.4 PDF for free.

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RD Sharma Class 9 Solutions Chapter 10 Exercise 10.4

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Question 1: In the figure, It is given that AB = CD and AD = BC. Prove that ΔADC ≅ ΔCBA.

Solution:

From the figure, AB = CD and AD = BC.

To prove: ΔADC ≅ ΔCBA

Consider Δ ADC and Δ CBA.

AB = CD [Given]

BC = AD [Given]

And AC = AC [Common side]

So, by the SSS congruence criterion, we have

ΔADC≅ΔCBA

Hence proved.

Question 2: In a Δ PQR, if PQ = QR and L, M, and N are the mid-points of the sides PQ, QR, and RP, respectively. Prove that LN = MN.

Solution:

Given: In Δ PQR, PQ = QR, and L, M, and N are the mid-points of the sides PQ, QR, and RP, respectively

To prove: LN = MN

Join L and M, M and N, N, and L

We have PL = LQ, QM = MR and RN = NP

[Since L, M, and N are mid-points of PQ, QR, and RP, respectively]

And also, PQ = QR

PL = LQ = QM = MR = PN = LR …….(i)

[ Using mid-point theorem]

MN ∥ PQ and MN = PQ/2

MN = PL = LQ ……(ii)

Similarly, we have

LN ∥ QR and LN = (1/2)QR

LN = QM = MR ……(iii)

From equations (i), (ii), and (iii), we have

PL = LQ = QM = MR = MN = LN

This implies, LN = MN

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