Preparing for the Regents Examination Geometry, AK

8 106
9 mA 75, mC 67
10 57
11 60
12 1. Perpendicular lines form right angles.
2. Right angles measure 90.
3. When two parallel lines are cut by a
transversal, corresponding angles are
congruent.
4. Congruent angles have equal measure.
5. Transitive property of congruence (3, 5)
6. If an angle measures 90, it is a right
angle.
7. If two lines intersect to form a right angle,
they are perpendicular.
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.)
13 1. ___
AB
2. 2 is supplement of 1.
3. 2 is supplement of 3.
4. 1 3 (If two angles are supplements
of the same angle, then they
are congruent.)
5. ___
BC ___
AD (When two lines are cut by
a transversal creating corresponding
angles, the lines are
congruent.)
14 1. ABC
2. ___
AB ___
BC
3. BAC BCA (Isosceles triangle
theorem)
4. _____
FHD ___
BC
5. FDA BCA (Corresponding
exterior angles are
congruent.)
6. _____
EHG ___
AB
7. BAC GEC (Corresponding
exterior angles are
congruent.)
8. GEC FDA
9. ___
HE ____
HD
10. EHD is isosceles. (Definition of
isosceles triangle)
46 Chapter 9: Parallel Lines
15 1. ___
DE ___
AC
2. 1 2 (Corresponding exterior
angles are congruent.)
3. 3 4
4. 2 3
5. 1 4 (Transitive property of
congruence)
16 1. ___
AC intersects ___
BD at E.
2. ___
AE ___
ED
3. A D
4. ___
AD ___
BC
5. A C (Alternate interior angles are
congruent.)
6. B D (Alternate interior angles are
congruent.)
7. B C (Transitive property of
congruence)
8. ___
AE ___
CE (Isosceles triangle
theorem)
9. ___
BE ___
DE
10. ___
AC ___
BD (Addition postulate)
17 1. n m
2. ABE and BAD are supplementary.
(Two interior angles on the
same side of the transversal
are supplementary.)
3. mABE mBAD 180
4. 1 _ mABE
2 1 _ mBAD 90
2
(Division postulate)
5. ___
BC bisects ABE.
6. mABC 1 _ mABE
2
(Definition of angle bisector)
7. ___
AC bisects BAD.
8. mACB 1 _ mBAD
2
( Definition of angle bisector)
9. mABC mACB 90
10. mBCA mABC mACB 180
11. mBCA 90
12. BCA is a right angle.
13. ___
BC ___
AC (Perpendicular lines form
right angles.)
18 1. r m and a b
2. 4 and 3 are supplementary.
3. 2 and 3 are supplementary.
4. (a) 4 2 (Supplements of the same
angle are congruent.)
5. 4 and 5 are supplementary.