Question

1. given that ca = cb and m∠cpb = 90 degrees, which statement can you conclude is true? ∠cap is a straight angle. cp is a perpendicular bisector. ap ≅ ac. cp bisects ac and cb.

Explanation:

Step1: Recall isosceles - triangle property

In $\triangle CAB$, since $CA = CB$, $\triangle CAB$ is an isosceles triangle.

Step2: Analyze the perpendicular condition

Given $\angle CPB=90^{\circ}$, and in an isosceles triangle, the line from the vertex (point $C$) to the mid - point of the base (line segment $AB$) is the perpendicular bisector. Here, $CP$ is perpendicular to $AB$. Also, in an isosceles triangle $\triangle CAB$ with $CA = CB$, the line $CP$ which is perpendicular to $AB$ bisects $AB$. So, $\overleftrightarrow{CP}$ is a perpendicular bisector.

Answer:

$\overleftrightarrow{CP}$ is a perpendicular bisector.