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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:DX¯≅EX¯

Key steps of proof:

a.ΔPOD≅ΔPOE

b.PD¯≅PE¯

c.ΔPDX≅ΔPEX

d.DX¯≅EX¯

Short Answer

Expert verified

a.ΔPOD≅ΔPOE

SAS postulate

b.PD¯≅PE¯

Corr. parts of≅Δ are ≅.

c.ΔPDX≅ΔPEX

SAS postulate

d.DX¯≅EX¯

Corr. parts of≅Δ are ≅.

Step by step solution

01

Step 1. Apply SAS postulate.

ConsiderΔPOD andΔPOE in whichOD¯≅OE¯,PO¯≅PO¯ and∠POD≅∠POE then by SAS postulate ΔPOD≅ΔPOE.

02

Step 2. Description of step.

As ΔPOD≅ΔPOE, by corresponding parts of congruent triangles, PD¯≅PE¯.

03

Step 3. Apply SAS postulate.

Consider ΔPDXand ΔPEX in whichPD¯≅PE¯,PX¯≅PX¯ and∠PXD≅∠PXE then by SAS postulate ΔPDX≅ΔPEX.

04

Step 4. Description of step.

As ΔPDX≅ΔPEX, by corresponding parts of congruent triangles, DX¯≅EX¯.

05

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

a.ΔPOD≅ΔPOE

SAS postulate

b.PD¯≅PE¯

Corr. parts of≅Δare ≅.

c.ΔPDX≅ΔPEX

SAS postulate

d.DX¯≅EX¯

Corr. parts of≅Δ are ≅.

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