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Leni [432]
3 years ago
9

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

Mathematics
2 answers:
adelina 88 [10]3 years ago
5 0

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.

QveST [7]3 years ago
3 0

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

ΔACE ≈ ΔBCD                               Angle angle similarity postulate

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

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