Question

Use the information below to find F such that triangle ABC is congruent with triangle DEF. A B equals 36, BC equals 24, D equals 48, M angle B equals 110, I am angle equals 110, EF equals?

Answer 1

Answer: ∠F = 23° and EF = 24

Explanation:

Since if two triangles are congruent,

Then, their corresponding sides and angles must be congruent.

Since, In Δ ABC and Δ DEF,

Sides AB, BC and CA are corresponding to sides DE, EF and FD respectively.

Also, ∠A, ∠B and ∠C are corresponding to ∠D, ∠E and ∠F respectively.

Therefore, If Δ ABC ≅ Δ DEF

⇒ AB ≅ DE , BC ≅ EF and CA ≅ FD

∠A ≅ ∠D, ∠B ≅ ∠E and ∠C ≅ ∠ F

But, It is given that AB = 36 and BC=24

Therefore, AB = DE = 36 and BC = EF = 24

Also, m∠B = 110° m∠D = 48°

⇒m∠E = 110° and m∠A = 48°

⇒m∠F = m∠C =180 - 158 = 23°