Question

Use the diagram and the information below to answer the question.

Given:
A
X
⊥
B
C
and
X
B
≅
X
C
Prove:
△
A
X
B
≅
△
A
X
C
image

Which statement is not part of the proof that shows
△
A
X
B
≅
△
A
X
C
?

A.
X
B
is congruent to
X
C
because it is given information.

B.
A
X
is congruent to
A
X
because of the reflexive property of congruence.

C.
∠
A
X
B

and
∠
A
X
C
are right angles because perpendicular lines form right angles.

D.
△
A
X
B
is congruent to
△
A
X
C
by the ASA Triangle Congruence Theorem.

Answer 1

D.

The triangles use XB ≅ XC (given), AX ≅ AX (reflexive), and ∠AXB and ∠AXC are right angles (perpendicular lines). Those give two sides and the included angle, so the correct congruence is by SAS, not ASA.