RD Sharma Solutions for Class 9 Mathematics Chapter 10 Exercise 10.4 Congruent Triangles are provided here. In this exercise, students will learn about the congruence criterion of triangles, mainly using SSS (Side-Side-Side). RD Sharma Solutions Class 9 Maths will also help students learn to solve problems stating the criteria for the congruence of two triangles. Get the detailed RD Sharma solutions from the below links.
RD Sharma Solutions for Class 9 Maths Chapter 10 Congruent Triangles Exercise 10.4
Access Answers to Maths RD Sharma Solutions for Class 9 Chapter 10 Congruent Triangles Exercise 10.4 Page Number 10.47
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
Hence Proved.
RD Sharma Solutions for Class 9 Maths Chapter 10 Congruent Triangles Exercise 10.4
RD Sharma Solutions Class 9 Maths Chapter 10 Congruent Triangles Exercise 10.4 is based on the topic- Congruence Criterion – SSS (Side-Side-Side). According to the criteria, two triangles are congruent if the three sides of one triangle are equal to the corresponding three sides of the other triangle.
Comments