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.
Given that AB = 10 inches, then ED = 10 inches.
Therefore, the statement that is not true is: