Preparing for the Regents Examination Geometry, AK

5. mAED m1
6. mAED m2 (Exterior angle
theorem)
7. m1 m2
10 1. mDCB mCBA (Exterior angle
theorem)
2. mCBA mCBM mMBA
3. mCBA mMBA
4. mDCB mMBA (Transitive postulate
of inequality)
11 12x 8 (4x 6) (7x 6)
x 8
12 12x 3 2 (5x 5) (5x 5)
x 11
13 Let x be mB, then mA is 3x.
3x x 104
x 26
mA 3x 3(26) 78
14 If the vertex angle of the triangle measures
130, each base angle measures 25 and
each exterior angle at the base measures
180 25 155.
7-4 Inequalities Involving
Sides and Angles of
Triangles
(page 133)
1 ZXY
2 PRQ
3 ___
AC
4 GFH
5 ___
KL
6 ACB
7 ___
YZ
8 mDGE mDEF mGDE, so
mDGE mGDE and DE EG.
9 PQS QSP, but QSP SQR, so
PQS SQR
10 m4 m3 m1, so m4 m1
Chapter Review (pages 133–136)
1 (3) p m p n
2 (3) 28
3 (2) an obtuse angle
4 True. Transitive postulate of inequality
5 True. Additive postulate of inequality
6 True. Postulate of inequality
7 False
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. m2 m3
2. m1 m2 (Exterior angle
theorem)
3. m1 m3 (Transitive postulate
of inequality)
9 1. BEST is a parallelogram.
2. BT BE
3. ___
BT ___
ES (Definition of a
parallelogram)
4. BT ES
5. ES BE (Substitution
postulate of
inequality)
10 1. ___
GS ___
GD
2. NPS RSP (Isosceles triangle
theorem)
3. mNPS mRSP
4. mISR mIPN
5. mISR mRSP mIPN mRSP
(Addition postulate
of inequality)
6. mISP mRSP mIPN mNPS
7. mISP mIPS (Postulate of
inequality)
11 1. mBCE mDBC
2. mACE mABD
3. mBCE mACE (Addition
mDBC mABD postulate
inequality)
4. mACB mABC (Postulate of
inequality)
12 1. ___
AD ___
DC
2. ACD CAD (Isosceles triangle
theorem)
3. mACD mCAD
4. mDAB mDCB
5. mDAB mACD ( Subtraction
mDCB mACD postulate of
inequality)
Chapter Review 37