Quadrilaterals Worksheet With Answers Page 37
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
50The proof of this theorem is as follows.
M
O
Given: Rhombus RHOM with diagonals MH and OR
P
P
Prove: MH ⊥ OR
Proof:
R
H
1. Rhombus RHOM with
1. Given
diagonals MH and OR
2. Definition of a rhombus
RM ≅
2.
MO
RP ≅
3. The diagonals of a rhombus bisect
3.
PO
each other.
MP ≅
4.
MP
4. Reflexive property
5. ∆RMP ≅ ∆OMP
5. SSS congruence postulate
6. ∠RPM ≅ ∠OPM
6. CPCTC
7. ∠RPM and ∠OPM are
7. Linear pairs are supplementary.
supplementary
∴Definition of supplementary ∠s
m∠RPM + m∠OPM = 180
9. Substitution
9. m∠RPM + m∠RPM = 180
2 m∠RPM = 180
10. x/÷ property of equality
10. m∠RPM = 90
11. A right ∠ has a measure of 90°
11. ∠RPM is a right angle
12. ⊥s form right ∠s
12. ∴ MH ⊥ OR
Note: The symbol ∴ means “therefore” and can be used in the last statement /conclusion.
Another property of a rhombus also involves the diagonals and will be proven as an
exercise.
Theorem
Either diagonal of a rhombus divides a pair
of opposite angles into two congruent angles.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education