Question

If a translation maps ∠D onto ∠B, which of the following statements is true? triangle CAB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED ΔCED ~ ΔCAB ΔCED ~ ΔCBA segment CD ≅ 2 segment CA segment CD ≅ 2 segment CB

Answer 1

Answer:

The correct option is;

ΔCED ~ ΔCAB

Step-by-step explanation:

Given that the translation maps angle ∠D to angle ∠B, we have;

Angle ∠D is congruent to ∠B (Given)

Segment ED is parallel to segment AB (lines having similar angles to a common transversal)

Therefore, ∠A is congruent to ∠E, (Angle on the same side of a transversal to two parallel lines)

∠C is congruent to ∠C reflexive property

Therefore, we have;

∠C ≅ ∠C

∠E ≅ ∠A  

∠D ≅ ∠B

Which gives ΔCED is similar to ΔCAB (not ΔCBA)