Question

In the figure, AD is perpendicular to BD, AC is perpendicular to BC, and AD ≅ BC.

Which of the following congruences is NOT necessarily true?
∠DAB ≅ ∠CBA
AE ≅ BE
AC ≅ BD
AD ≅ AE
∠EAB ≅ ∠EBA

Answer 1

D) AD ≅ AE

Explanation:

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Answer 2

• D) AD ≅ AE

Explanation:

According to given details the triangles ADB and BCE are congruent as per HL congruence

Lets verify the choices

∠DAB ≅ ∠CBA,

• this is true as corresponding angles of congruent triangles

AE ≅ BE,

• this is true as AEB is isosceles

AC ≅ BD,

• this is true as corresponding sides of congruent triangles

AD ≅ AE,

• this is NOT true as AE > AD as hypotenuse of right triangle is greater than legs

∠EAB ≅ ∠EBA,

• this is true as AEB is isosceles