Question

Is DEF = ABC? If so, type the reason, if not type no.​

Answer 1

Yes

Explanation:

All you need to do is figure out the missing angles. We know that the three angles in a triangle add up to 180 degrees.

For angle B in ABC, 180-52-39= 89. So angle B = 89 degrees.

For angle D in DEF, 180-39-89= 52. So angle D = 52 degrees.

Then see if the order of the angles match up.

DEF = 52 degrees, 89 degrees, 39 degrees

ABC = 52 degrees, 89 degrees, 39 degrees

The order of the same angles match, so triangle DEF and triangle ABC are equal.

Answer 2

Yes, triangle DEF is similar to triangle ABC because their corresponding angles are the same size.

Explanation:

Interior angles of a triangle sum to 180°.

⇒ ∠A + ∠B + ∠C = 180°

⇒ 52° + ∠B + 39° = 180°

⇒ ∠B = 89°

⇒ ∠D + ∠E + ∠F = 180°

⇒ ∠D + 89° + 39° = 180°

⇒ ∠D = 52°

Two triangles are similar if their corresponding angles are the same size.

If ΔDEF ~ ΔABC then:

• ∠D = ∠A
• ∠E = ∠B
• ∠F = ∠C

From inspection of the given diagram:

• ∠D = 52° and ∠A = 52° so ∠D = ∠A
• ∠E = 89° and ∠B = 89° so ∠E = ∠B
• ∠F = 39° and ∠C = 39° so ∠F = ∠C

Therefore, the triangles are similar because their corresponding angles are the same size.