Question

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

Answer 1

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