Question

Are the two triangles below similar?

Answer 1

Answer:

Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

Two triangles ABC and DEF are given .

The measure of angles in triangle ABC are:

m<A=30°,m< C=65°,

m<B= 180-(30+65)=85°(measure of sum of angles in any triangle is 180°)

In triangle DEF the measure of the angles are :

m<D=30°,m<E=85°,m<F=180-(30+85)=65°(sum of angles in a triangle add to 180°)

In triangles ABC and DEF,

< A=<D=30°

<B=<E=85°

<C=<F=65°

The two triangles are similar by AAA property.

Answer 2

Answer :- Yes the two triangles are similar because there are two pairs of congruent corresponding angles.

Explanation:-

In Δ ABC

∠A=30° , ∠C=65 °

By angle sum property of triangle

∠A + ∠B + ∠C= 180°

⇒∠B= 180°-∠A-∠C=180°-30°-65°=85°

⇒∠B=85°

Now in ΔABC and ΔDEF

∠A=∠D=30° and ∠B=∠E=85°

⇒ there are two pairs of congruent corresponding angles.

So by AA-similarity criteria

ΔABC ≈ ΔDEF