Download Review Sheet Aims 27-33 Math 10H 1. Write always, sometimes, or

Review Sheet Aims 27-33
Math 10H
1. Write always, sometimes, or never.
a) If one angle of a parallelogram is a right angle, all the other angles are right
angles.
b) The diagonals of a rectangle are perpendicular.
c) The diagonals of a square bisect each other.
d) If a quadrilateral is equilateral, it is a rhombus.
e) The diagonals of an equiangular quadrilateral are congruent.
#2-5 Multiple Choice
2. Which statement is false?
(a) All parallelograms are quadrilaterals.
(b) All rectangles are parallelograms.
(c) All squares are rhombuses.
(d) All rectangles are squares.
3. In quadrilateral ABCD, the diagonals bisect its angles. If the diagonals are not
congruent, quadrilateral ABCD must be a
(a) square
(b) rectangle
(c) rhombus
(d) cannot determine
4. From which given information can you conclude that RSTW is a parallelogram?
(a) RS ll WT, RS ≅ ST
(b) RS ll WT, ST ≅ RW
R
W
(c) RS ≅ ST, RW ≅ WT
Z
(d) RZ ≅ TZ, SZ ≅ WZ
S
T
5. In the diagram of ΔABC, D is the midpoint of AB,
and E is the midpoint of BC.
If AC = 4x + 10, which expression represents DE?
(a) x + 2.5 (b) 2x + 5 (c) 2x + 10 (d) 8x + 20
6. If you choose a polygon at random from the following set
{rectangle, rhombus, parallelogram, square}, what is the probability you
choose a polygon that…
a) is equilateral? _____
b) has congruent diagonals and congruent sides? _____
c) has at least one pair of opposite sides parallel? ______
d) has perpendicular diagonals? _____
e) has no congruent sides? ______
7. The lengths of the diagonals of a rhombus are 14 and 48.
Find the perimeter of the rhombus.
8. QRST is a parallelogram. The measure of ≮Q is 40 less than three times the
measure of ≮S. Find m≮R.
9. For what value(s) of x is the figure the given special parallelogram?
a) rectangle
b) rhombus
c) square
(3x+6)o
(5x+2)o
(8x+7)o
3x
(x2 ­ 4x)o
o
10. In rhombus ABCD with diagonals AC and DB, the perimeter is 52.
If the length of diagonal AC is 10, what is the length of DB?
11. In parallelogram ABCD, m≮A = 2z + 20 and m≮D = 3z - 15. Show that
parallelogram ABCD is a rectangle.
12. In parallelogram ABCD, AB = 2x + 3, BC = 4x - 5, and CD = 5x - 9. Show that
parallelogram ABCD is a rhombus.
R
Statements
T
W
13. Given: RSTW and SXTW are parallelograms.
Prove: ΔRSW ≅ ΔSXT
S
Reasons
X
14. In parallelogram ABCD, diagonals AC and BD intersect at E.
If m≮BAE = 5x - 5, m≮ABE = 3x + 13, and m≮BDC = 2x + 32.
a) Is ABCD a rhombus? Justify your answer.
b) Is ABCD a square? Justify your answer.
14
15. Find the perimeter of the triangle formed by connecting
10
the midpoints of the sides of ΔABC.
16
C
16. D, E, and F are the midpoints of AB, BC and CA,
respectively. If AB = 20, BC = 12, and AC = 16,
what is the perimeter of quadrilateral ABEF?
F
E
A
B
17. In ΔABC, D is the midpoint of AB and E is the
midpoint of BC. If AC = 3x - 15 and DE = 6,
find the value of x.
D
E
A
C
K
18. Given: FGJK is a rectangle; ≮1 ≅ ≮2.
Prove: a) KJ ll EH
b) KE ≅ JH
Statements
1
E
B
D
F
J
2
G
H
Reasons
END
D
19. Given: ABCD is a rhombus,
MB ≅ NB
Prove: MD ≅ ND
A
C
M
N
B
Statements
20. Given: XYRS is a rectangle,
XM ≅ SM
Prove: M is the midpoint of YR.
Statements
Reasons
X
Y
M
R
S
Reasons
21. Complete the proof.
Given: AC bisects ≮DAB,
A
1 2
6
B
DB bisects ≮ADC,
4
AB ll DC
Prove: ABCD is a rhombus.
5
D
3
C
Reasons
Statements
Numbers in
parentheses
are step
numbers.
1. AC bisects ≮DAB, DB bisects ≮ADC 1. Given
2.
3. AB ll DC
4. ≮2 ≅ ≮3, ≮5 ≅ ≮6
2.
3. Given
4.
5. ≮
,≮ ≅≮
≅≮
6. AD ≅ DC, AD ≅ AB
5. Substitution Property
(2,4)
6.
(5)
7.
7. same as (5)
8. ABCD is a parallelogram.
8.
9. ABCD is a rhombus.
9.
(3,7)
22. The diagonal of a rectangle is 3 more than the length. The width of the
rectangle is 6 less than the diagonal. Find the width, length, perimeter, and area
of the rectangle.
V
W
P
Y
X
Q
23. Given: VPQY is a rectangle,
VX ≅ WY
Prove: VWXY is a rectangle.
Statements
Reasons
D
24. C is the centroid of ΔDEF. If GF = 12x2 + 6y,
write an expression, in
simplest form, to represent CF.
G
C
F
H
25. Use the diagram from #24 where C is the centroid of ΔDEF.
If DC = x2 and CH = x + 12, find both possible lengths of DH.
E