Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK
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4. A A<br />
5. ADE ABC<br />
b<br />
(AA)<br />
AC _ <br />
AB<br />
AE _<br />
AD<br />
c 32<br />
5 a Each smaller triangle is similar to <strong>the</strong><br />
larger triangle so <strong>the</strong>y are similar to each<br />
o<strong>the</strong>r.<br />
b Corresponding sides of similar triangles<br />
are in proportion.<br />
c Product of means product of extremes.<br />
d BD 6<br />
6 1. MAH is a right angle.<br />
2. −−<br />
UT −−−<br />
AH<br />
3. UTH is a right angle.<br />
4. MAH UTH<br />
5. H H<br />
6. MAH UTH (AA)<br />
7. MA _ <br />
AH<br />
UT _<br />
TH (Corresponding<br />
sides of similar<br />
triangles are in<br />
7 1.<br />
proportion.)<br />
−−<br />
AB −−<br />
DE<br />
2. CAB CED (Alternate interior<br />
angles are<br />
congruent.)<br />
3. ACB ECD (Vertical angles are<br />
congruent.)<br />
4. ACB ECD (AA)<br />
5. AB _ <br />
ED<br />
AC _<br />
EC<br />
6. AB _ AC<br />
<br />
ED _<br />
EC (Corresponding<br />
sides of similar<br />
triangles are in<br />
proportion.)<br />
8 1. EBA CDA<br />
2. A A<br />
3. EBA CDA<br />
4. BCF DEF<br />
5. −−<br />
AC −−<br />
AE<br />
6. DEC BCE (Isosceles triangle<br />
<strong>the</strong>orem)<br />
7. DEC DEF (Subtraction<br />
BCE BCF<br />
8. FEC FCE<br />
9. CBD EDB<br />
postulate)<br />
10. CBD EDB<br />
11.<br />
(AA)<br />
BC _ <br />
BE<br />
DE _<br />
DC<br />
76 Chapter 12: Ratios, Proportion, and Similiarity<br />
12. BC DC (The product of <strong>the</strong><br />
BE DE means equals <strong>the</strong><br />
product of <strong>the</strong><br />
extremes.)<br />
9 1. EBC CDE<br />
2. BFC DFE (Vertical angles are<br />
congruent.)<br />
3. DEF BCF (AA)<br />
4. FB _ <br />
FD<br />
FC _<br />
FE<br />
5. FB _ FC<br />
<br />
FD _ (Corresponding sides<br />
FE<br />
of similar triangles are<br />
in proportion.)<br />
10 1. −−<br />
AE −−<br />
BC<br />
2. ADC and EDC are right angles.<br />
3. ADC EDD<br />
4. DAC DEC<br />
5. DEC DAC (AA)<br />
6. EC _ AC<br />
_<br />
ED<br />
AD<br />
7. EC AD (The product of <strong>the</strong><br />
AC ED means equals <strong>the</strong><br />
product of <strong>the</strong><br />
extremes.)<br />
11 1. Isosceles triangle WXZ with −−−<br />
WX −−−<br />
WZ<br />
2. X Z<br />
3. YTW YRW<br />
4. XTY ZRY (Supplements of congruent<br />
angles are<br />
congruent.)<br />
5. XTY ZRY (AA)<br />
6. YT _ <br />
YR<br />
XY _<br />
ZY<br />
7. YT _ <br />
XY<br />
YR _ (Corresponding sides<br />
ZY<br />
of similar triangles are<br />
in proportion.)<br />
12 1. Rectangle DEFG<br />
2. DGB and EFC are right angles.<br />
3. DGB EFC<br />
4. Isosceles triangle ADE<br />
5. BDG CEF (Supplements of congruent<br />
angles are<br />
congruent.)<br />
6. BDG CEF (AA)<br />
7. DG _ BG<br />
<br />
EF _ (Corresponding sides<br />
CF<br />
of similar triangles are<br />
in proportion.)
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