1. The document provides examples for finding measures of angles, sides, and other quantities of parallelograms, trapezoids, and kites. 2. It gives step-by-step instructions to draw a parallelogram with a given angle measure and to use properties of parallelograms to find other angle measures. 3. The document also includes examples of finding side lengths of parallelograms using known angle measures or diagonal lengths.

2. 1. Describe the angles, sides and other
quantities involving parallelogram
2. Find the measure of angles, sides and
other quantities involving
parallelogram
3. Show patience in finding the
measure of angles and sides of a
parallelogram

3. Write C for Congruent, S for
Supplementary ,P for Parallel , B
for Bisect each other to
describe the angles , sides and
diagonals of a parallelogram

8. Illustrative Example 1:
Follow the procedure below to find the
measure of angles, sides and other
quantities involving parallelogram,
trapezoids and kites

9. a. ∠𝑀measures 60° , Extend the rays
of M, and draw parallelogram on the
grid paper, remember opposite angles
are congruent
𝑚∠ 𝑁 = 120°, 𝑚∠ 𝑀 = 60°,
𝑚∠ 𝑂 =______ and
m ∠P=_________

10. M
N
O
P
60°

12. b. WXYZ is a parallelogram, using what you know
about parallelograms,
𝑋𝑊 ∥ 𝑌𝑍, 𝑚∠𝑋𝑊 = 𝑚∠𝑌𝑍
𝑋𝑌 ∥ 𝑊𝑍, 𝑚∠𝑋𝑌 = 𝑚∠𝑊𝑍
What is ∠𝑋𝑌 𝑎𝑛𝑑 𝑚∠𝑌𝑍 ?
𝑚∠𝑊𝑋𝑌= 113°. Use what you know about angles in a
parallelogram to find the measure of the other angles.
𝑚∠𝑋𝑌𝑍= ______°;
𝑚∠𝑌𝑍𝑊= ______;
𝑚∠𝑍𝑊𝑋° = ______

14. c. Juan measured some segments in
Problem b. He found that 𝑚∠𝑊𝑌 = 8cm
and 𝑚∠𝑀𝑍 = 3 cm.
Give the lengths of the following segments:
𝑚∠𝑊𝑀 =____cm,
𝑚∠𝑀𝑌 = ____cm,
𝑚∠𝑋𝑀 = ____cm,
𝑚∠𝑋𝑍 = ____cm

16. d. Diagonals 𝐽𝐿 and 𝑀𝐾 bisect each other.
a) The midpoint of 𝐽𝐿 is P.
b) Another line 𝑀𝐾 passing through P so that
𝑀𝑃 ≅ 𝐾𝑃.
c) What quadrilateral did you form using MJKL.
d) If 𝑀𝑃=4, what is 𝑃𝐾?

19. 7.
a.If 𝑚∠ 𝐸𝐿𝑂 = 115°
Find 𝑚∠LOV
𝑚∠EVO
b. Why did you say so?
8.
a.𝑃𝐼 = 4 and 𝐿𝑃 = 6
What is 𝐾𝑃 & 𝑃𝐸
b. Why?
9.
a. If 𝑆𝑈 = 20
What is 𝐸𝑅?
b. Why?

24. 𝟏
𝟒
𝒔𝒉𝒆𝒆𝒕 𝒐𝒇 𝒑𝒂𝒑𝒆𝒓
Choose the letter of the
best answer. Write your in
CAPITAL form.

25. 1. What is the
measure of ∠2
in rhombus
HOME?
a. 75° c. 105°
b. 90° d. 180°

26. 2. Two consecutive angles of a
parallelogram have measures
(𝑥 + 30)° and [2(𝑥 – 30)]° .
What is the measure of the
smaller angle?
a. 15° b. 30° c. 60° d. 80°

27. 3. In rhombus
RHOM, what is
the measure of
∠ROH?
a. 35° c. 55°
b. 45° d. 90°

28. 4. In rectangle KAYE, YO = 18
cm. Find the length of diagonal
AE.
a. 6 cm c. 18 cm
b. 9 cm d. 36 cm

29. Assignment # 3.___

30. B. Given: Quadrilateral POST is an isosceles
trapezoid with OS || PT. ER is its median.
a. If 𝑂𝑆 = 3𝑥 – 2, 𝑃𝑇 = 2𝑥 + 10 and 𝐸𝑅 =
14, how long is each base?
b. If m ∠ 𝑃 = 2𝑥 + 5 and 𝑚∠ 𝑂 = 3𝑥 – 10,
what is m ∠ T?
c. One base is twice the other and ER is 6 cm
long. If its perimeter is 27 cm, how long is each
leg?

31. d. 𝐸𝑅 is 8.5 in long and one leg
measures 9 in. What is its perimeter
if one of the bases is 3 in more than
the other?