Quadrilaterals Worksheet With Answers Page 5
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50a) Press F5 and select Measure-angle.
b) Select a point on one of the sides of the angle, the vertex, and a point on
the other side of the angle to be measured followed by ENTER after each
selection.
c) Move the “hand” to position the angle measure on the figure and press
ENTER.
d) Compare the measures of opposite angle pairs. How do these results
compare to the conjecture made? Refer to the example in figure 4.
figure 4
The measures of the opposite angles in
ABCD are congruent as shown in
figure 4. These results can be stated in the following theorem.
Theorem
The opposite angles of a parallelogram
have the same measure and are congruent.
A paragraph-style proof of this theorem is given below.
Given:
ABCD
D
C
Prove: ∠ A ≅ ∠ C
∠ B ≅ ∠ D
A
B
Proof:
AB ≅
AD ≅
Draw auxiliary line DB. We have
DC
and
BC
(Opposite sides of a
DB ≅
parallelogram are congruent.)
DB
by the reflexive property. It follows
that ∆ ABD ≅ ∆ CDB by the SSS congruence postulate. By CPCTC, ∠ A ≅ ∠ C.
To prove ∠ B ≅ ∠ D, draw auxiliary line AC and prove ∆ ADC ≅ ∆ CBA by the
SSS congruence postulate.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education