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Skills Practice Workbook - Glencoe

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15–5<br />

Two-Column Proofs<br />

Write a two-column proof.<br />

<strong>Skills</strong> <strong>Practice</strong><br />

1. Given: �ITC is an isosceles triangle with base<br />

I�C�, TS �� bisects �ITC<br />

Prove: I�S� � C�S�<br />

Proof:<br />

Statements Sample Answer: Reasons<br />

a. �ITC is an isosceles triangle a. Given<br />

with base I�C�.<br />

b. TS �� bisects �ITC b. Given<br />

c. I�T� � C�T� c. Definition of isosceles triangle<br />

d. �ITS � �CTS d. Definition of angle bisector<br />

e. S�T� � S�T� e. Reflexive Property<br />

f. �ITS � �CTS f. SAS<br />

g. I�S� � C�S� g. CPCTC<br />

2. Given: ABCD is a square.<br />

Prove: A�C� � B�D�<br />

Proof:<br />

NAME DATE PERIOD<br />

Statements Sample Answer: Reasons<br />

a. ABCD is a square. a. Given<br />

b. A�D� � B�C� b. Definition of a square<br />

c. �ADC and �BCD are right c. Definition of a square<br />

angles.<br />

d. �ADC � �BCD d. Definition of congruent angles<br />

e. D�C� � D�C� e. Reflexive Property<br />

f. ΔADC � ΔBCD f. SAS<br />

g. A�C� � B�D� g. CPCTC<br />

© <strong>Glencoe</strong>/McGraw-Hill 89 Geometry: Concepts and Applications<br />

I<br />

D<br />

T<br />

S<br />

A B<br />

C<br />

C

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