RD Sharma class 9 Mathematics chapter 10 exercise 10.4 Congruent Triangles solutions are provided here. In this exercise, students will learn about congruence criterion of triangles mainly using SSS (Side-Side-Side). RD Sharma Class 9 Maths will also help students learn to solve problems and stating the criteria for the congruence of two triangles. Get the detailed RD Sharma solutions from the below link.
Access Answers to Maths RD Sharma Class 9 Chapter 10 Congruent Triangles Exercise 10.4 Page number 10.47
Question 1: In figure, It is given that AB = CD and AD = BC. Prove that ΔADC ≅ ΔCBA.
From 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 SSS congruence criterion, we have
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.
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 equation (i), (ii) and (iii), we have
PL = LQ = QM = MR = MN = LN
This implies, LN = MN
RD Sharma Solutions for Class 9 Maths Chapter 10 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.