216k views
2 votes
Is DEF = ABC? If so, type the reason, if not type no.​

Is DEF = ABC? If so, type the reason, if not type no.​-example-1

2 Answers

5 votes

Answer:

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.

User Carlos Quiroga
by
8.5k points
1 vote

Answer:

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.

User Liad
by
9.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories