In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if
a. BC = EF
b. AC = DE
c. AC = EF
d. BC = DE

Solution:

The triangles ABC and DEF are

It is given that

AB = FD and ∠A = ∠D

For a triangle to be congruent from the SAS axiom two sides and included angle must be equal

For ∆ ABC ≅ ∆ DFE from SAS axiom we require AC = DE

Therefore, the two triangles will be congruent by the SAS axiom if AC = DE.

✦ Try This: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

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

NCERT Exemplar Class 9 Maths Exercise 7.1 Problem 11

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if , a. BC = EF, b. AC = DE, c. AC = EF, d. BC = DE

Summary:

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if AC = DE

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