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GEOMETRY
4-#13
Review – Quadratics
Name: ___________________
Period: _____
To complete each definition, find the appropriate word in the second column.
a.
b.
c.
d.
e.
f.
g.
h.
i.
parallelogram
trapezoid
square
base angles
isosceles trapezoid
rectangle
consecutive angles
kite
rhombus
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.
3
10.
3
11.
2
38°
12.
3
2
63°
79°
1
2
37°
1
99°
Find the values for the variables for which ABCD must be a parallelogram.
13.
A
14.
A (3y – 20)° (4y+4)° B
B
O
C
(2x+6)°
(4x)°
D
D
15.
C
For the trapezoids and kites, find the measures of angles 1 and 2.
a)
2
77°
b)
1
54°
82°
2
1
c)
d)
62°
2
22°
2
1
112°
1
AO  3 y  3
BO  4x  2
CO  3x
DO  3 y  1
16.
In rhombus ABCD, AB = 6, AC = 8, and mABC  30.
a) mADC  _______
b) mAEB  ______
c) BC = _____
d) AE = ______
e) mBAD  ______
f) mCDE  ______
17.
Given:
Prove:
18.
A
E
D
C
R
parallelogram SPQR and
S
SQ bisects PQR
SQ bisects PSR
P
Q
Complete the following proof by filling in the blanks
Q
R
T
S
Given: QRST is a rectangle
Prove: QS  RT
Statements
Reasons
1. QRST is a rectangle
2. QT  RS
3. QTS and RST are right angles
4. QTS  RST
5. TS  TS
6.  ____   ____
7. QS  RT
Factor the following:
19.
x 2  3 x  28
20.
x 2  13 x  42
21. 2 x 2  x  36
22.
3 x 2  13x  10
B
23. Solve for x and y:
3x  4 y  9

x  2 y  7
2 x  3 y  2

24. 5 x  3 y  26
25. Find the area of the triangle:
2.5cm
4cm
2cm
5cm
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?
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.
What is the length of c?
32. Find the area of the shaded portion of the
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
13. x=29, y = 28
12. Angle 1 = 38, angle 2 = 43, angle 3 = 99
14. x = 4, y = 5
15. A. Angle 1 = 103, angle 2 = 77 b. angle 1 = angle 2 = 22
angle 2 = 118
c. angle 1 = 68, angle 2 = 90
d. angle 1 = 68,
16. A 30 b. 90 c. 6 d. 4 e. 150 f. 15
parallelogram SPQR and
17.
SQ bisects PQR
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)
24 (4, -2)
27. 216 m^2
25. 5 cm^2
28. 950 m^2
21. (2x-9)(x+4) 22. (3x-2)(x+5)
23. (5, 6)
26. 55 cm^2
29. 252 cm^2 30. 12 in
31. 27 in 32. 40 cm^2