In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are
a. isosceles but not congruent
b. isosceles and congruent
c. congruent but not isosceles
d. neither congruent nor isosceles
Solution:
The two triangles ABC and PQR are
We know that
∠A + ∠B + ∠C = ∠P + ∠Q + ∠R
It is given that
∠C = ∠P and ∠B = ∠Q … (1)
We get
∠A + ∠B + ∠C = ∠C + ∠B + ∠R
Here ∠A = ∠R
Using the AAA criterion
∆ ABC ≅ ∆ PQR
As AB = AC, ∆ ABC is an isosceles triangle
∠B = ∠C [opposite angles of equal sides]
From (1), ∠P = ∠Q
So ∆ PQR is an isosceles triangle
As the relation between sides of two triangles is unknown, congruency cannot be proved using SAS or ASA
Therefore, the two triangles are isosceles but not congruent.
✦ Try This: In triangles DEF and XYZ, DE = DF, ∠F = ∠X and ∠E = ∠Y. The two triangles are a. isosceles but not congruent, b. isosceles and congruent, c. congruent but not isosceles , d. neither congruent nor isosceles
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7
NCERT Exemplar Class 9 Maths Exercise 7.1 Problem 10
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are , a. isosceles but not congruent , b. isosceles and congruent , c. congruent but not isosceles , d. neither congruent nor isosceles
Summary:
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are isosceles but not congruent
☛ Related Questions:
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