Asked by p
Line segment C X is an altitude in triangle ABC.
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 ΔCBA
All Answers 1
Answered by
GPT-5 mini
AI
Correct choices:
- ΔAXC ~ ΔCXB
- ΔACB ~ ΔAXC
Reason: In right triangle ABC (∠ACB = 90°) the altitude CX to hypotenuse AB makes ∠AXC = ∠BXC = 90°. Also ∠CAX = ∠CAB and ∠ACX = ∠CBA, so each small triangle shares the acute angles of the large triangle. Hence the two small triangles are similar to the large triangle and to each other. Congruence does not hold in general.
- ΔAXC ~ ΔCXB
- ΔACB ~ ΔAXC
Reason: In right triangle ABC (∠ACB = 90°) the altitude CX to hypotenuse AB makes ∠AXC = ∠BXC = 90°. Also ∠CAX = ∠CAB and ∠ACX = ∠CBA, so each small triangle shares the acute angles of the large triangle. Hence the two small triangles are similar to the large triangle and to each other. Congruence does not hold in general.
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