Question

CX is an altitude in triangle ABC. Which statements are true? Check all that apply.

ΔABC ~ΔBXC
ΔAXC ~ ΔCXB
ΔBCX ~ ΔACX
ΔACB ~ ΔAXC
ΔCXA ~ ΔCBA

Answer 1

Answer:

ΔAXC ~ ΔCXB ; and ΔACB ~ ΔAXC  

Step-by-step explanation:

We must match up corresponding angles in the similarity statements.

∠A in ΔAXC will match ∠A in ΔABC as well as ∠C in ΔCXB.

∠X in ΔAXC will match ∠C in ΔABC as well as ∠X in ΔCXB.

∠C in ΔAXC will match ∠B in ΔABC as well as ∠B in ΔCXB.

Using this information, the only ones that match are ΔAXC ~ ΔCXB  and ΔACB ~ ΔAXC.

Answer 2

In geometry, similar triangles may or may not have congruent corresponding side lengths.

The true similarity statements are:  ΔAXC ~ ΔCXB  and ΔACB ~ ΔAXC.

Given that:

Length CX is an altitude in triangle ABC

This means that length CX divides triangle ABC into smaller triangles.

So, we have

• Angles A and C are similar angles in triangles AXC and CXB
• Angles X is present in triangles AXC and CXB
• Angles C and B are similar angles in triangles AXC and CXB

Hence, the true similarity statements are:  ΔAXC ~ ΔCXB  and ΔACB ~ ΔAXC.

Read more about similar triangles at:

https://brainly.com/question/2644832