Geo_Book_Answers
Geo_Book_Answers
Geo_Book_Answers
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1.<br />
A<br />
LESSON 13.4<br />
Use x to represent the measures of one pair of<br />
congruent angles and y for the other pair. Use the<br />
Quadrilateral Sum Theorem and the division<br />
property to get x y 180°. Therefore, the<br />
opposite sides are parallel by the Converse of the<br />
Interior Supplements Theorem.<br />
2. D C<br />
A<br />
Use the AIA Theorem, the reflexive property, and<br />
the SAS Congruence Postulate to get ADC <br />
CBA. Then use CPCTC and the Converse of the<br />
AIA Theorem to get AB DC .<br />
3. D C<br />
A<br />
Use the definition of rhombus, the reflexive<br />
property,and the SSS Congruence Postulate to get<br />
ABC ADC. Then use CPCTC and the<br />
definition of angle bisector to prove that AC bisects<br />
DAB and BCD. Repeat the steps above using<br />
diagonal DB.<br />
4. D C<br />
A<br />
Use the definition of parallelogram to get AD BC<br />
and AB DC . Then use the Interior Supplements<br />
Theorem.<br />
5. D C<br />
A<br />
D C<br />
1<br />
7<br />
8<br />
1<br />
2<br />
4<br />
3<br />
2<br />
6 5<br />
4<br />
3<br />
B<br />
4<br />
1<br />
B<br />
B<br />
3 2<br />
B<br />
B<br />
Use the reflexive property and the SSS Congruence<br />
Postulate to get ABD CDB. Then use<br />
CPCTC and the Converse of the AIA Theorem to<br />
get AB CD and AD CB. Therefore,ABCD is a<br />
rhombus by the definitions of parallelogram and<br />
rhombus.<br />
6.<br />
D<br />
A<br />
Use the Converse of the Opposite Angles Theorem<br />
to prove that ABCD is a parallelogram. Then use<br />
the definition of rectangle.<br />
7. D<br />
C<br />
A<br />
Use the definition of rectangle to prove that ABCD<br />
is a parallelogram and DAB CBA. Then use<br />
the Parallelogram Opposite Sides Theorem, the<br />
reflexive property, and the SAS Congruence Postulate<br />
to get DAB CBA. Finish with CPCTC.<br />
8. D<br />
C<br />
A<br />
Use the Parallelogram Opposite Sides Theorem,<br />
the reflexive property, and the SSS Congruence<br />
Postulate to get DAB CBA. Repeat the above<br />
steps to get ADC CBA and DAB BCD.<br />
Then use CPCTC and the transitive property to get<br />
DAB ABC BCD ADC. Finish with<br />
the Four Congruent Angles Rectangle Theorem.<br />
9. D<br />
C<br />
A E<br />
Use the Parallel Postulate to construct DE CB.<br />
Then use the Parallelogram Opposite Sides<br />
Theorem and the transitive property to prove that<br />
AED is isosceles. Therefore, A B by the<br />
Isosceles Triangle Theorem, the CA Postulate, and<br />
substitution.<br />
10. D<br />
C<br />
A<br />
C<br />
B<br />
B<br />
B<br />
B<br />
B<br />
Use the Isosceles Trapezoid Theorem, the reflexive<br />
property, and the SAS Congruence Postulate to get<br />
DAB CBA. Then AC BD by CPCTC.<br />
ANSWERS TO EXERCISES 149<br />
<strong>Answers</strong> to Exercises
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