Preparing for the Regents Examination Geometry, AK

2 1. PQ PS
2. ___
PQ −−
PS
3. 1 2
4. m1 m2
5. m1 m3
(Isosceles triangle
theorem)
6. m2 m3
3 1. CE BD
2. CF BF
3. CE CF FE
4. CF FE BD
5. BD BF FD
(Substitution
postulate of
inequality)
6. CF FE BF FD
7. BF FE BF FD
8. BF FE BF (Subtraction
BF FD BF postulate of
or FE FD
4 1.
inequality)
___
AE ___
EB
2. ABE BAE
3. mABE mBAE
4. mDAB mCBA
(Isosceles triangle
theorem)
5. mDAB mCAD mBAE
6. mCAD mBAE mCBA
7. mCBA mABE mDBC
8. mCAD mBAE
mABE mDBC
9. mCAD mABE
mABE mDBC
10. mCAD mABE (Subtraction
mABE mABE postulate of
mDBC mABE
or mCAD mDBC
5 1. C is the midpoint of
inequality)
−−
AB .
2. AC CB
3. AB AC CB
4. AB AC AC
or AB 2AC
5. AB _ AC
2
6. F is the midpoint of −−
DE .
7. DF DF
8. DE DF FE
9. DE DF DF
or DE 2DF
10. DE _ DF
2
11. AC DF
12. AB _ DF
2
13. AB _
DE
2 _
2
14. AB _ 2
DE
2 _
2 2 (Multiplication
or AB DE postulate of
equality.)
6 1. RP 3RS
2. RP _ 3RS
3 _
3
or RP _ RS
3
3. RQ 3RT
4. RQ _ 3RT
3 _
3
or RQ _ RT
3
5. RS RT
6. RP _ RT
3
7. RP _ RQ
3 _
3
8. RP _ RQ
3
3 _ 3 (Multiplication
3
or RP RQ postulate of
equality.)
7 1. I is the midpoint of −−
EH .
2. EH EI IH
3. EI IH
4. EH EI EI
EH 2EI
5. J is the midpoint of −−
EF .
6. EF EJ JF
7. EJ JF
8. EF EJ EJ
or EF 2EJ
9. EH EF
10. 2EI EF
11. 2EI 2EJ
12. EI EJ (Division postulate
of equality)
8 1. ___
BD bisects ABC.
2. ABD DBC (Definition of
bisector)
3. mABD mDBC
4. mABC mABD mDBC
5. mABC mABD mABD
or mABC 2mABD
6. −−
BD bisects ADC.
7. ADB BDC
8. mADB mBDC
9. mADC mADB mBDC
10. mADC mADB mADB
or mADC 2mADB
7-1 Basic Inequality Postulates 35