Preparing for the Regents Examination Geometry, AK

6. mDAB mCAD
mDCB mACD
7. mCAB mACB (Postulate of
inequality)
13 1. PQRS is a parallelogram.
2. SP RQ (Definition of
parallelogram)
3. ST TP RQ
4. ST TP QU RU
or ST RU QU TP
5. TP QU
6. 0 QU TP (Subtraction
postulate of
inequality)
7. 0 ST RU
8. ST RU (Addition
postulate of
inequality)
14 ___
ST
15 ___
AB
16 ___
AB
17 ___
BC
18 −−
DE
19 AD BD
20 mB 120
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.)
21 1. ___
AD bisects CAB.
2. ___
BE bisects CBA.
3. mDAB mEBA
4. mDAB 2 mEBA 2 (Multiplication
postulate of
inequality)
5. mCAB 2(mDAB) (Definition
of bisector)
6. mCBA 2(mEBA) (Definition
of bisector)
7. mCAB mCBA
38 Chapter 7: Polygon Sides and Angles
22 1. CF AE
2. CF 2 AE 2 (Multiplication postlate
of inequality)
3. F is the midpoint of ___
CD .
4. CF 2 CD (Definition of
midpoint)
5. CD AE 2
6. E is the midpoint of ___
AB .
7. AB AE 2 (Definition of
midpoint)
8. CD AB (Multiplication postulate
of inequality)
23 1. AC CB
2. AC _
2
CB
_
2
3. AD AC _
2
4. AD CB _
2
5. BE CB _
2
(Division postulate of
inequality)
(Definition of
midpoint)
(Definition of
midpoint)
6. AD BE
24 Let A be the acute angle and let B be
its supplement. mB 180 mA. Since
mA 90, mB 90 and is therefore
obtuse by the subtraction postulate of
inequality.
25 Let C be the complement of A, and
let D be the complement of B. mC
90 mA and mC mD by the subtraction
postulate of inequality.
26 m1 m3 because an exterior angle is
greater than either nonadjacent interior angle
and m1 m2. So m2 m3 by the
substitution postulate of inequality.
27 mABC mABD because a whole is
greater than its parts. mBAC mABC
because they are opposite congruent sides
of a triangle. So mBAC mABD by the
substitution postulate of inequality, and
DB DA because the greater side lies
opposite the greater angle.