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Geometry
Notes – 8.3
Name_________________________
Parallelograms, Rhombuses, Rectangles, and Squares
parallelogram –
If a quadrilateral is a parallelogram, then…
- its opposite sides are congruent.
- its opposite angles are congruent.
- its consecutive angles are supplementary.
- its diagonals bisect each other.
Examples 1- 2:
1. Find the values of x and y.
2. Find the indicated measure given the JKLM is a parallelogram.
a. NM
b. KM
c. m  JML
d. m  KML
Practice 3 – 4:
3. Find the values of x and y.
4. Find the indicated measures in parallelogram ABCD.
a. m  BCD
B
100
C
E
b. If BE = 9, find BD.
37
A
D
How do I know/PROVE if a quadrilateral is a parallelogram?
If….
- both pairs of opposite sides of a quadrilateral are congruent
- both pairs of opposite angles of a quadrilateral are congruent
- the diagonals of a quadrilateral bisect each other
- one pair of opposite sides of a quadrilateral are congruent and parallel
Examples 5 – 6: For what value of x is the quadrilateral a parallelogram?
5.
6.
Practice 7 – 8: For what value of x is the quadrilateral a parallelogram?
7.
rhombus –
rectangle –
square –
8.
A parallelogram is a rhombus if and only if…
(properties of a rhombus)
- its diagonals are perpendicular
- each diagonal bisects a pair of opposite angles
A parallelogram is a rectangle if and only if…
(properties of a rectangle)
- its diagonals are congruent
Examples 9 – 12: Classify the special quadrilateral. Then find the values of x and y.
9.
10.
11.
12.
Examples 13 – 18: The diagonals of rhombus ABCD intersect at E. Given that
mBAC  53 and DE = 8, find the indicated measure.
13. mDAC
14. mAED
15. mADC
16. DB
17. AE
18. AC
Examples 19 – 24: The diagonals of rectangle QRST intersect at P. Given that
mPTS  34 and QS = 10, find the indicated measure.
19. mSRT
20. mQPR
21. QP
22. RP
23. QR
24. RS
Practice 25 – 30: The diagonals of square LMNP intersect at K. Given that LK = 1, find
the indicated measure.
25. mMKN
26. mLMK
27. mLPK
28. KN
29. MP
30. LP
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