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

A). AC ≅ BC

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