GEOMETRY
GEOMETRY 4-#13 Name: ___________________
Review – Quadratics Period: _____
To complete each definition, find the appropriate word in the second column.
1. A(n) ________ is a parallelogram with four right angles.
2. A(n) _________ is a quadrilateral with two pairs of adjacent
sides congruent and no opposite sides congruent.
3. Angles of a polygon that share a common side are _______.
4. A(n) ________ is a quadrilateral with exactly one pair of
parallel sides.
5. A(n) _______ is a parallelogram with four congruent sides.
6. A(n) ________ is a quadrilateral with both pairs of opposite
sides parallel.
7. A(n) ________ is a parallelogram with four congruent sides and four right angles
8. A(n) ________ is a trapezoid whose nonparallel sides are congruent.
9. Two angles that share a base of a trapezoid are its _________.
Find the measures of the numbered angles for each parallelogram.
10. 11. 12.
Find the values for the variables for which ABCD must be a parallelogram.
13. 14.
15. For the trapezoids and kites, find the measures of angles 1 and 2.
a) b)
c) d)
16. In rhombus ABCD, AB = 6, AC = 8, and [pic]
a) [pic] b) [pic]
c) BC = _____ d) AE = ______
e) [pic]______ f) [pic]______
17.
Given: [pic]
Prove: [pic]
18. Complete the following proof by filling in the blanks
Given: QRST is a rectangle
Prove: [pic]
Factor the following:
19. [pic] 20. [pic] 21. [pic] 22. [pic]
23. Solve for x and y: [pic] 24. [pic]
25. Find the area of the triangle:
26. Find the area of the parallelogram: 27. Find the area of the trapezoid:
28. If the perimeter of the rectangle is 126m, what is the area?
[pic]
29. Find the area of the kite. 30. In the trapezoid below, what is the length
of the short base:
31. The area of the trapezoid is 273 in2. 32. Find the area of the shaded portion of the
What is the length of c? trapezoid:
For the Quadrilaterals test you may use 1 pg handwritten notes (front and back) and your beige sheet. I suggest that you use either the “Quadrilaterals Resource Page” notes that we did in class or the Quadrilaterals “tree,” but you could also make your own page. You may also use a calculator.
ANSWERS:
1. F 2. H 3. G 4. B 5. I 6. A 7. C 8. E 9. D
10. Angle 1=angle 3 =101, angle 2 = 19, angle 3 = 101
11. Angle 2 = angle 3= 26 12. Angle 1 = 38, angle 2 = 43, angle 3 = 99
13. x=29, y = 28 14. x = 4, y = 5
15. A. Angle 1 = 103, angle 2 = 77 b. angle 1 = angle 2 = 22 c. angle 1 = 68, angle 2 = 90 d. angle 1 = 68, angle 2 = 118
16. A 30 b. 90 c. 6 d. 4 e. 150 f. 15
17. [pic]given, use opposite sides of a parallelogram are congruent by def’n of a parallelogram and that SQ is congruent to itself by the reflexive prop of congruence. Then triangle PSQ is congruent to triangle RQS by SSS. Then angle PSQ is congruent to angle RQS by CPCTC. Angle PQS is congruent to angle RQS by definition of angle bisector. Angle RSQ is congruent to angle PSQ by transitive property of congruence and SQ bisects angle PQR by definition of angle bisector.
18. given, opp sides of a rectangle are congruent, def. of rectangle, all right angles are congruent, reflexive property of congruence, triangle QTS and triangle RST are congruent by SAS, CPCTC
19. (x+4)(x-7) 20 (x-7)(x-6) 21. (2x-9)(x+4) 22. (3x-2)(x+5) 23. (5, 6)
24 (4, -2) 25. 5 cm^2 26. 55 cm^2
27. 216 m^2 28. 950 m^2 29. 252 cm^2 30. 12 in 31. 27 in 32. 40 cm^2
-----------------------
a. parallelogram
b. trapezoid
c. square
d. base angles
e. isosceles trapezoid
f. rectangle
g. consecutive angles
h. kite
i. rhombus
2
38°
3
3
2
3
63°
99°
1
37°
79°
1
2
A
B
(3y – 20)°
[pic]
[pic]
[pic]
[pic]
A
(4y+4)°
B
O
C
D
C
(2x+6)°
(4x)°
D
1
2
1
77°
54°
82°
2
62°
2
1
22°
2
1
112°
A
E
D
B
C
R
S
P
Q
R
Q
S
T
|Statements |Reasons |
|1. QRST is a rectangle | |
|2. [pic] | |
|3. [pic] and [pic]are right angles | |
|4. [pic] | |
|5. [pic] | |
|6. [pic] | |
|7. [pic] | |
4cm
2cm
5cm
2.5cm
................
................
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