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In Exercises 1-6 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.

Prove:NE¯≅OS¯

Key steps of proof:

a.ΔRNX≅ΔLOY

b.∠X≅∠Y

c.ΔNEX≅ΔOSY

d.NE¯≅OS¯

Short Answer

Expert verified

a.ΔRNX≅ΔLOY

SSS postulate

b.∠X≅∠Y

Corr. parts of≅Δ are ≅.

c.ΔNEX≅ΔOSY

SAS postulate

d.NE¯≅OS¯

Corr. parts of≅Δ are ≅.

Step by step solution

01

Step 1. Apply SSS postulate.

ConsiderΔRNX andΔLOY in which RN¯≅LO¯,NX¯≅OY¯ andRX¯≅LY¯ then by SSS postulate ΔRNX≅ΔLOY.

02

Step 2. Description of step.

As ΔRNX≅ΔLOY, by corresponding parts of congruent triangles, ∠X≅∠Y.

03

Step 3. Apply SAS postulate.

Consider ΔNEXand ΔOSYin which NX¯≅OY¯,EX¯≅SY¯ and∠X≅∠Y then by SAS postulate ΔNEX≅ΔOSY.

04

Step 4. Description of step.

As ΔNEX≅ΔOSY, by corresponding parts of congruent triangles, NE¯≅OS¯.

05

Step 5. Give the reason for each key step of the proof.

a.ΔRNX≅ΔLOY

SSS postulate

b.∠X≅∠Y

Corr. parts of≅Δ are ≅.

c.ΔNEX≅ΔOSY

SAS postulate

d.NE¯≅OS¯

Corr. parts of≅Δ are ≅.

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