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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 21 and 22, complete each proof.

Given: R S ¯ T Q ¯
Prove: R T S Q
PROOF
Statements Reasons
1. R S ¯ T Q ¯ 1. ?
2. S T . 2. ?
3. ? . 3. If two s are , the s are = in measure.
4. m S = 1 2 m T R . 4. ?
5. m T = 1 2 ( m S Q ) 5. ?
6. 1 2 ( m R T ) = 1 2 ( m S Q ) 6. ?
7. m R T = m S Q 7. Multiplication Property of
Equality.
8. ? 8. If two arcs of a are = in measure the arcs are .

To determine

To prove:

RTSQ.

Explanation

Given:

RS¯TQ¯

Proof:

PROOF
Statements Reasons
1. RS¯TQ¯ 1. Given
2. ST. 2. Interior alternative angles are always equal.
3. mS=mT. 3. If two s are , the s are = in measure.
4. mS=12(mRT). 4. By theorem, the measure of an inscribed angle of a circle is half the measure of its intercept arc.
5. mT=12(mSQ) 5

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