Honors Geometry; 11/21

We continued working on parallelogram proofs today by going over a couple more together in class.  The method of finding congruent triangles first was used in each example, and the triangles were found to be congruent by using the various properties of parallelograms.

Our chapter 5 quiz (5.1 to 5.3) is tomorrow in class.


Assignment:  Chapter 5 Quiz review sheet


Chapter 5 Review Packet answer key

Lesson 5-1 practice worksheet

1.  both pairs of opposite angles congruent in parallelograms
2.  diagonals bisect in parallelograms
3.  both pairs of opposite sides congruent in parallelograms
4.  both pairs of opposite sides congruent in parallelograms

5.  WX = 15
6.  angle WXY = 110
7.  XP = 13
8.  WY = 36
9.  angle WXY = 105
10.  angle WZY = 120

11.  angle STP = 112
12.  angle PSR = 100
13.  angle PQR = 100
14.  angle PSQ = 25

15  QR = 19
16.  RS = 25
17.  x = 6
18.  angle P = 105
19.  x = 16
20.  x = 7

Two column proof

Statements                                                     Reasons
ABCD is parallelogram                                 given
P is midpoint of AB                                       given
Q is midpoint of DC                                      given
AP parallel to DQ                                          opp. sides of large parallelogram parallel
AP = 1/2 AB                                                  midpoint theorem
DQ = 1/2 DC                                                 midpoint theorem
AB = DC                                                       opp. sides of large parallelgram congruent
AP = DQ                                                       transitive
AP congruent DQ                                         def. of congruent
APDQ is parallelogram                                if one pair of sides is both parallel and
                                                                      congruent, then figure is parallelogram

Lesson 5-2 Practice worksheet

1.  yes;  both pairs of opposite sides are congruent
2.  yes;  both pairs of opposite sides are parallel
3.  yes;  one pair of opposite sides are both congruent and parallel
4.  no conclusion possible
5.  yes;  diagonals bisect each other
6.  yes;  both pairs of opposite sides are congruent
7.  yes;  both pairs of opposite angles are congruent

8.  x = 25;  y = 11
9.  x = 95;  y = 85

10.  AB = 4;  BC = 6;  CD = 4;  AD = 6
11.  AB = 7;  BC = 5;  CD = 7;  AD = 5

12.  two column proof

Statements                                                        Reasons
angle W and angle X are supp.                        given
angle X and angle Y are supp.                         given
angle Y and angle Z are supp.                          given
m angle W + m angle X = 180                     def. of supplementary
m angle X + m angle Y = 180                      def. of supplementary
m angle X + m angle Y = m angle X + m angle W      substitution
m angle Y = m angle W                                subraction prop. =
angle Y is congruent to angle W                   def. of congruence
m angle Y + m angle Z = 180                        def. of supplementary
m angle X + m angle Y = m angle Y + m angle Z     substitution
m angle X = m angle Z                                  subtraction prop. =
angle X is congruent to angle Z                    def. of congruence
WXYZ is parallelogram                               if both pairs of opp. angles are congruent,
                                                                     then figure is parallelogram

Theorems involving parallel lines practice worksheet   (odd problems only)

1.  true
2.  false
3.  true
4.  true
5.  x = 20, y = 10
6.  x = 5, y = 3
7.  15
8.  27
9.  6
10.  2a
11.  84
12.  70
13.  72
14.  7
15.  16
16.  6
17.  2

Practice 18:  Parallelograms

1.  4
2.  5
3.  120
4.  20
5.  3
6.  7
7.  105
8.  x = 10
9.  x = 6
10.  always
11.  always
12.  sometimes
13.  never
14.  x = 11,  y = 16
15.  x = 26,  y = 15
16.  x = 11, y = 4