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Chapter 2: Q11 (page 40)

Copy everything shown and supply missing statements and reasons.

Given:

m∠1=m∠3;

m∠2=m∠4

Prove: m∠ABC=m∠DEF

Proof:

Short Answer

Expert verified

If a=band c=d, then a+c=b+d.

m∠1+m∠2=m∠3+m∠4

Step by step solution

01

Step 1. Apply the addition property of algebra.

If a=band c=d, then a+c=b+d.

m∠1+m∠2=m∠3+m∠4

02

Step 2. Angle addition postulate.

From the given figure, it can be observed that some of m∠1and m∠2gives m∠ABC, that is m∠1+m∠2=m∠ABC.

From the given figure, it can be observed that some of m∠3and m∠4gives m∠DEF, that is m∠3+m∠4=m∠DEF.

03

Step 3. Apply substitution property.

Substitute m∠ABCfor m∠1+m∠2and m∠DEFfor m∠3+m∠4in step 1.

m∠1+m∠2=m∠3+m∠4m∠ABC=m∠DEF

Hence, it is proved that m∠ABC=m∠DEF.

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