Question

It is given that ∆ABC ≅ ∆FDE and AB = 6cm, ∠B = 80° and ∠A= 40°. What is the length of side DF of ∆FDE ? What is the measure of ∠E ?​

Answer 1

WE KNOW-

Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

GIVEN-

Triangle ABC is congruent to triangle FDE

AB=6cm

∠B = 80° and ∠A= 40°

TO DETERMINE-

• the length of side DF of ∆FDE
• the measure of ∠E

SOLUTION-

We know that the sum of 3 angles in a triangle is 180°.

Hence,

∠A+∠B+∠C=180°

=40°+80°+∠C=180°

=∠C=60°

Since triangle ABC is congruent to triangle FDE

so , the corresponding sides are equal in length and the corresponding angles are equal in size for the two triangls ABC and FDE.

therefore,

∠E=∠C=60°

DF=AB=6cm

Hence,

DF=6 cm and ∠E=60∘ is satisfied.

hope it helps you:)

Answer 2

Answer:

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