RD Sharma Solutions for Class 9 Mathematics Chapter 10 Exercise 10.2 Congruent Triangles are provided here. The RD Sharma solutions have been systematically prepared to help the Class 9 students to tackle all Chapter 10 Maths problems. The solutions consist of solved questions along with detailed explanations, which have been designed by subject experts at BYJU’S. Students can easily access the PDFs of RD Sharma Solutions for Class 9 from the links given below to have an overview of the chapter.
RD Sharma Solutions for Class 9 Maths Chapter 10 Congruent Triangles Exercise 10.2
Access Answers to RD Sharma Solutions for Class 9 Maths Chapter 10 Congruent Triangles Exercise 10.2 Page Number 10.21
Question 1: In the figure, it is given that RT = TS, ∠ 1 = 2 ∠ 2 and ∠4 = 2(∠3). Prove that ΔRBT ≅ ΔSAT.
Solution:
In the figure,
RT = TS ……(i)
∠ 1 = 2 ∠ 2 ……(ii)
And ∠ 4 = 2 ∠ 3 ……(iii)
To prove: ΔRBT ≅ ΔSAT
Let the point of intersection RB and SA be denoted by O
∠ AOR = ∠ BOS [Vertically opposite angles]
or ∠ 1 = ∠ 4
2 ∠ 2 = 2 ∠ 3 [From (ii) and (iii)]
or ∠ 2 = ∠ 3 ……(iv)
Now in Δ TRS, we have RT = TS
⇒ Δ TRS is an isosceles triangle
∠ TRS = ∠ TSR ……(v)
But, ∠ TRS = ∠ TRB + ∠ 2 ……(vi)
∠ TSR = ∠ TSA + ∠ 3 ……(vii)
Putting (vi) and (vii) in (v), we get
∠ TRB + ∠ 2 = ∠ TSA + ∠ 3
⇒ ∠ TRB = ∠ TSA [From (iv)]
Consider Δ RBT and Δ SAT
RT = ST [From (i)]
∠ TRB = ∠ TSA [From (iv)]
By the ASA criterion of congruence, we have
Δ RBT ≅ Δ SAT
Question 2: Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
Solution: Lines AB and CD Intersect at O
Such that BC ∥ AD and
BC = AD …….(i)
To prove: AB and CD bisect at O.
First, we have to prove that Δ AOD ≅ Δ BOC
∠OCB =∠ODA [AD||BC and CD is transversal]
AD = BC [from (i)]
∠OBC = ∠OAD [AD||BC and AB is transversal]
By ASA Criterion:
Δ AOD ≅ Δ BOC
OA = OB and OD = OC (By c.p.c.t.)
Therefore, AB and CD bisect each other at O.
Hence Proved.
Question 3: BD and CE are bisectors of ∠ B and ∠ C of an isosceles Δ ABC with AB = AC. Prove that BD = CE.
Solution:
Δ ABC is isosceles with AB = AC, and BD and CE are bisectors of ∠ B and ∠ C We have to prove BD = CE. (Given)
Since AB = AC
⇒ ∠ABC = ∠ACB ……(i)
[Angles opposite to equal sides are equal]Since BD and CE are bisectors of ∠ B and ∠ C
∠ ABD = ∠ DBC = ∠ BCE = ECA = ∠B/2 = ∠C/2 …(ii)
Now, Consider Δ EBC = Δ DCB
∠ EBC = ∠ DCB [From (i)]
BC = BC [Common side]
∠ BCE = ∠ CBD [From (ii)]
By ASA congruence criterion, Δ EBC ≅ Δ DCB
Since corresponding parts of congruent triangles are equal.
⇒ CE = BD
or, BD = CE
Hence proved.
RD Sharma Solutions for Class 9 Maths Chapter 10 Congruent Triangles Exercise 10.2
RD Sharma Solutions for Class 9 Maths Chapter 10 Congruent Triangles Exercise 10.2 is based on the topic Criterion of Congruence – ASA ( Angle-Side-Angle). According to the criteria, two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and included side of the other triangle.
