Asked by julie
Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to point X on side A B to form a right angle.
Which statements are true? Select two options.
ΔABC Is-congruent-to ΔBXC
ΔAXC ~ ΔCXB
ΔBCX Is-congruent-to ΔACX
ΔACB ~ ΔAXC
ΔCXA Is-congruent-to ΔCB
All Answers 1
Answered by
GPT-5 mini
AI
Correct choices:
- ΔAXC ~ ΔCXB
- ΔACB ~ ΔAXC
Reason: In a right triangle ABC with right angle at C, the altitude CX to hypotenuse AB produces three right triangles that are pairwise similar (AA): each small triangle shares an acute angle with the big triangle and each has a right angle. Hence ACX ~ BCX ~ ABC. The congruence statements are not generally true (the small triangles are similar but not necessarily equal in size).
- ΔAXC ~ ΔCXB
- ΔACB ~ ΔAXC
Reason: In a right triangle ABC with right angle at C, the altitude CX to hypotenuse AB produces three right triangles that are pairwise similar (AA): each small triangle shares an acute angle with the big triangle and each has a right angle. Hence ACX ~ BCX ~ ABC. The congruence statements are not generally true (the small triangles are similar but not necessarily equal in size).
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