35.5k views
0 votes
If ΔJAB ≅ ΔFED, AB = 10 in, m∠BJA = 52º, and m∠EDF = 65º, which of the following statements is not true?

A.
m∠ABJ = 65º
B.
ED = 10 in
C.
∠B ≅∠E
D.
m∠FED = 63º

1 Answer

2 votes

Answer:

C. ∠B ≅∠E

Explanation:

Since ΔJAB ≅ ΔFED, their corresponding angles are congruent.

Therefore:

  • ∠J ≅ ∠F → m∠BJA ≅ m∠DFE
  • ∠A ≅ ∠E → m∠JAB = m∠FED
  • ∠B ≅ ∠D → m∠ABJ ≅ m∠EDF

Given that m∠BJA = 52° and m∠EDF = 65°, then:

  • m∠BJA = m∠DFE = 52°
  • m∠ABJ = m∠EDF = 65°

Therefore, m∠ABJ = 65°.

Interior angles in a triangle sum to 180°. Therefore:

⇒ m∠JAB + m∠BJA + m∠ABJ = 180°

⇒ m∠JAB + 52° + 65° = 180°

⇒ m∠JAB + 117° = 180°

⇒ m∠JAB = 63°

As m∠JAB = m∠FED, then m∠FED = 63°.

Since ΔJAB ≅ ΔFED, their corresponding sides are congruent.

  • AB = ED
  • BJ = DF
  • AJ = EF

Given that AB = 10 inches, then ED = 10 inches.

Therefore, the statement that is not true is:

  • ∠B ≅∠E
User Khalid Ali
by
7.3k points