Question

Drag an expression or phrase to each box to complete the proof.

Answer 1

<4 ≅ <1, 3 <≅ 2                              Corresponding angles postulate

ΔACE ≈ ΔBCD                               Angle angle similarity postulate

(CB + BA)/CB = (CD + DE)/CD      Substitution property of equality

Answer 2

Answer:

1st blank: ∠4≅∠1 and ∠3≅∠2      

2nd blank: Angle-Angle similarity postulate

3rd blank: Substitution property of equality.

Step-by-step explanation:

Consider the provided figure.

Statement                                                                Reason

ΔACE, BD║AE                                                          Given

∠4≅∠1 and ∠3≅∠2                                      Corresponding angle postulate

ΔACE $\sim$ ΔBCD                             Angle-Angle similarity postulate

$\frac{CA}{CB}=\frac{CE}{CD}$                                      Definition of similar triangles

CA=CB+BA and CE=CD+DE                     Segment addition postulate

$\frac{CB+BA}{CB}=\frac{CD+DE}{CD}$                        Substitution property of equality.

$\frac{CB}{CB}+\frac{BA}{CB}=\frac{CD}{CD}+\frac{DE}{CD}$                                      Addition of fractions.

$1+\frac{BA}{CB}=1+\frac{DE}{CD}$                                      Simplification of fractions

$\frac{BA}{CB}=\frac{DE}{CD}$                                      Subtraction property of equality.