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Chapter 2: Q14 (page 42)

Copy everything shown and write a two-column proof.

Given:m∠SRT=m∠STR;

m∠3=m∠4

Proof:m∠1=m∠2

Short Answer

Expert verified

Statements

Reasons

1.

Given

2.

2. Angle addition postulate

3.

3. Substitution property

4.

4. Given

5.

5. Subtraction property

Step by step solution

01

Step 1. Angle addition postulate.

From the given figure, it can be observed that sum of m∠1and m∠3gives m∠SRT, that is m∠2+m∠4=m∠STR.

From the given figure, it can be observed that sum of m∠2and m∠4gives m∠STR, that is m∠2+m∠4=m∠STR.

02

Step 2. Apply substitution property.

Substitute m∠1+m∠3for m∠SRTand m∠2+m∠4for in m∠STR.

m∠SRT=m∠STRm∠1+m∠3=m∠2+m∠4

03

Step 3. Apply the subtraction property of algebra.

If a=band c=d, then a−c=b−d.

m∠1=m∠2

04

Step 4. Write a two-column proof.

Write a two-column proof with the help of the above-mentioned steps.

Statements

Reasons

1.m∠SRT=m∠STR

Given

2.m∠1+m∠3=m∠SRT;m∠2+m∠4=m∠STR

2. Angle addition postulate

3.m∠1+m∠3=m∠2+m∠4

3. Substitution property

4.m∠3=m∠4

4. Given

5.m∠1=m∠2

5. Subtraction property

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Most popular questions from this chapter

State the converse of each conditional. Is the converse true or false?

If , then .

Copy everything shown and supply missing statements and reasons.

Given:

m∠1=m∠3;

m∠2=m∠4

Prove: m∠ABC=m∠DEF

Proof:

Justify each statement with a property from algebra or property of congruence.

IfRS=TW then TW=RS.

State which postulate, definition, or theorem justifies the statement about the diagram.

BD+DC=BC

Copy everything shown and supply missing statements and reasons.

Given:ST=RN;IT=RU

Prove: SI=UN

Proof;
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