Preparing for the Regents Examination Geometry, AK

6. BAC DAE 6. Transitive
property.
7. mBAC
mDAE
7. If two angles are
congruent, their
measures are
equal.
9 Statements Reasons
1. 8 x y 1. Given.
2. y 3 2. Given.
3. 8 x 3 3. Substitution
property.
4. x 3 8 4. Symmetric
property.
10 Statements Reasons
1. M is the midpoint
of −−
AB .
1. Given.
2. −−−
AM −−−
MB 2. A midpoint
divides a line
segment into two
congruent line
segments.
3. −−−
MB −−
BC 3. Given.
4. −−−
AM −−
BC 4. Transitive
property.
3-6 Remaining Postulates
of Equality
(pages 51–52)
1 Partition postulate of equality
2 Division postulate of equality
3 Addition postulate
4 Subtraction postulate
5 Division postulate of equality
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.)
10 Chapter 3: Introduction to Geometric Proof
6 1. m1 m2
2. m3 m4
3. m1 m3 m2 m4
4. mDAB m1 m3
mBCD m2 m4
5. mDAB mBCD (Substitution
7 1.
postulate)
−−
AB −−
CB
2. −−−
AD −−
CE
3. AB CB
4. AD CE
5. AB AD CB CE
6. DB EB
7. −−
DB −−
EB
8 1. AB AC
2. AD
(Line segments
that are equal in
measure are congruent.)
1 _ AC
3
3. AE 1 _ AB
3
4. AD AE (Division
postulate)
9 1. mEAB mFBC
2. AG is the angle bisector of EAB.
3. BH is the angle bisector of FBC.
4. m1 1 _ mEAB
2
5. m2 1 _ mFBC
2
6. m1 m2
10 1. AB DE
2. AC 3AB
3. DF 3DE
(Division
postulate)
4. AC DF (Multiplication
postulate)
Chapter Review (page 52)
1 Reflexive property of equality
2 Transitive property of equality
3 Symmetric property of equality
4 mBAD 1 _ mBAC
2