Preparing for the Regents Examination Geometry, AK

11. mABC mADC
12. 2mABD 2mADB
13. mABD mADB
(Division postulate of equality)
9 1. AE 1 _ AC
3
2. AE 3 1 _
AC 3 or 3AE AC
3
(Multiplication postulate of equality)
3. AD 1 _ AB
3
4. AD 3 1 _
AB 3
3
or 3AD AB
5. AC AB
6. 3AE 3AD (Substitution postulate)
7. AE AD (Division postulate of
inequality)
10 1. ___
AE is the median from A to ___
BC .
2. E is the midpoint of ___
BC .
(Definition of median)
3. BE EC (Definition of midpoint)
4. BC BE EC
5. BC BE BE
or BC 2BE
6. ___
CD is the median from C to ___
AB .
7. D is the midpoint of ___
AB .
(Definition of median)
8. AD DB
9. AB AD DB
10. AB AD AD
or AB 2AD
11. AB BC
12. 2AD 2BE
13. AD BE (Division postulate of
inequality)
7-2 The Triangle Inequality
Theorem
(page 128)
1 Yes
2 No
3 Yes
4 No
5 Yes
6 No
36 Chapter 7: Polygon Sides and Angles
7 Yes
8 Yes
9 Yes
10 Yes
11 1 S 9
12 6 S 10
13 2.5 S 5.5
14 0 S 12
15 1 1 _ S 3
2 1 _
2
7-3 The Exterior Angles
of a Triangle
(pages 130–132)
1 (2) isosceles
2 (4) right
3 a CAD
b ABC and ACB
c mCAD mABC; mCAD mACB
4 a True
b True
c True
d True
5 6 and 9
6 5, 9, 8, and 10
7 7 and 10
Note: Since there are many variations of proofs,
the following is simply one set of acceptable
statements to complete each proof. Depending
on the textbook used, the wording and format
of reasons may differ, so they have not been
supplied for the method of congruence applied
in each problem. (These solutions are intended
to be used as a guide—other possible solutions
may vary.)
8 1. m1 m3 (Exterior angle
theorem)
2. m3 m5 (Exterior angle
theorem)
3. m1 m5 (Transitive postulate
of inequality)
9 1. ___
AB ___
CD
2. 1 is a right angle.
3. AED is a right angle.
4. AED 1 (Right angles are
congruent.)