Question

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

Answer 1

Answer:

i. ΔAXC ~ ΔCXB

ii. ΔBCX Is-congruent-to ΔACX

Step-by-step explanation:

From the given ΔABC, CX is the altitude of ΔABC; and also an angle bisector of <ACB.

So that:

m<AXC = m<BXC (right angle property)

m<ACX = m<BCX (congruent property)

m<ACX + m<AXC + m<CAX = $180^{o}$ (sum of angles in a triangle)

m<BCX + m<BXC + m<CBX = $180^{o}$ (sum of angles in a triangle)

Therefore, from the figure it can be deduced that;

i. ΔAXC ~ ΔCXB (Angle-Angle-Side, AAS, property)

ii. ΔBCX Is-congruent-to ΔACX (Angle-Angle-Side, AAS, property)

Answer 2

Answer:

ΔAXC ~ ΔCXB

ΔACB ~ ΔAXC

Step-by-step explanation:

B and D are correct