29.7k views
25 votes
Given that CD is the perpendicular bisector of AB, which of the following statements can be used to show that AC=BC?​

Given that CD is the perpendicular bisector of AB, which of the following statements-example-1
User AndrewVos
by
3.7k points

1 Answer

8 votes

Answer:

B. ΔAXC ≅ ΔBXC by SSS, so AC ≅ BC because they are corresponding parts of congruent triangles.

Explanation:

From the given diagram, XC is common to ΔAXC and ΔBXC.

And it can be observed that CD divides AB into two equal length segments.

Thus,

AX ≅ BX (bisection property of a line)

AC ≅ BC (congruence property of triangles)

Therefore, the congruence relationship between triangles ΔAXC and ΔBXC would be, Side-Side-Side (SSS) so as to show that AC ≅ BC.

User Michael Boselowitz
by
3.7k points