Question

What can be determined from the diagram?
A) AC≅BC
B) AP≅CP
C) AC≅AP
D) ∠ACP ≅ ∠CAP

It's a triangle with a line going straight down the middle label P

A is the corner to the left
C is corner at top
B is corner at the right
P is between A and B
P creates a 90 degree angle

Answer 1

I am pretty sure the right answer is a

Answer 2

Answer:

A). AC ≅ BC

Step-by-step explanation:

Given triangle ACB is bisected at C by CP making 90 degree at P making two triangles,  Δ ACP and  Δ BCP

It is given in the diagram that AP = PB and ∠APC = ∠BPC = 90°

Since, CP is common to both the triangles, Δ ACP and  Δ BCP.

Therefore, Δ ACP is similar to Δ BCP.

                    AP = PB

                   CP = CP

                ∠APC = ∠BPC

Therefore Δ ACP is similar to Δ BCP by side, side, angle (SSA)

And since Δ ACP and Δ BCP are similar, therefore AC = BC

Thus, AC ≅ BC