Question

ab ≅ bc and ad ≅ cd
what additional information would make it immediately possible to prove
that triangles axb and cxb are congruent using the hl theorem?
b x and d x are congruent.
a x and c x are congruent.
a c and b d are perpendicular.
b d bisects angle a b c
make it immediately possible to prove
congruent using the sss congruence
theorem?
a x and c x are congruent.

Explanation:

Step1: Recall HL theorem

HL (Hypotenuse - Leg) theorem states that if the hypotenuse and a leg of a right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.

Step2: Analyze triangles \(AXB\) and \(CXB\)

We know that \(AB\cong BC\) (given). For triangles \(AXB\) and \(CXB\) to be right - triangles and use the HL theorem, we need to know that \(\angle AXB=\angle CXB = 90^{\circ}\). If \(AC\perp BD\), then \(\angle AXB=\angle CXB = 90^{\circ}\).

Answer:

\(AC\) and \(BD\) are perpendicular.