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Chapter 2: Q9 (page 42)

Copy everything shown and supply missing statements and reasons.

Given: DW=ON

Prove: DO=WN

Proof:

Short Answer

Expert verified

From the given figure, it can be observed that some of DOand OWgives DW, that is DW=DO+OW.

From the given figure, it can be observed that some of OWand WNgives ON, that is ON=OW+WN.

Step by step solution

01

Step 1. Apply segment addition postulate.

From the given figure, it can be observed that some of DOand OWgives DW, that is DW=DO+OW.

From the given figure, it can be observed that some of OWand WNgives ON, that is ON=OW+WN.

02

Step 2. Apply Substitution property.

Substitute DO+OWfor DWand OW+WNfor ONin DW=ON.

DW=ONDO+OW=OW+WN

03

Step 3. Reflexive property of congruence.

By reflexive property, OW=OW.

04

Step 4. Apply subtraction property of algebra to step 2.

If a=band c=d, then a鈭�c=b鈭�d.

DO+OW=OW+WNDO=WN

Hence, it is proved that DO=WN.

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