Download Chapter 6 Supplemen

Honors Geometry
Chapter 6 Supplement
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1. Given: PQ || RS
Q
mRQS = (4x)°
mPQS = (5x)°
mRSQ = 40°
mPSQ = 32°
Find the value of x, mPQS, mSQR, mSPQ
R
(4x)°
(5x)°
40°
32°
P
2. Given: AD || BC
A
mD = (8x + 20)°
mA = (150 – 6x)°
mC = (12x + 60)°
S
B
a) Find the value of x and mB.
D
C
b) Is AB || CD ?
S
3. Given: parallelogram PSTM
mP = (2x + y)°
mM = (3x + 5y)°
mT = (4x – 3y + 8)°
Find the values of x, y, mP, and mS.
T
P
4. Given: FRAM is a rectangle
mR = (6x + 3y)°
mF = (10x + 15y)°
Find the values of x and y.
M
F
R
M
A
A
5. Given: MAST is a rhombus
mMAT = (x2)°
mSAT = (6x + 40)°
Fimd mMAS.
S
M
T
6. Given: PSQF is a trapezoid
PS || FQ
mP = (3x2)°
mQ = (3x)°
mF = (12x)°
Find mS.
P
F
S
Q
7. PRY is equilateral and has a perimeter of 72.
Find the perimeter of parallelogram CART.
R
A
T
P
Y
C
8. The angles of a rhombus are 60 and 120. The short diagonal is 8 cm. Find the perimeter of the rhombus.
9. Fill in the table:
Property
Both pair opposite
sides parallel
Exactly 1 pair opposite
sides parallel
Diagonals
perpendicular
Diagonals congruent
Diagonals bisect each
other
Both pairs opposite
sides congruent
Exactly 1 pair of
opposite sides
congruent
All sides congruent
Both pair opposite
angles congruent
Exactly 1 pair opposite
angles congruent
All angles congruent
Both pair of opposite
angles supplementary
At least one right angle
Parallelogram
Rectangle
Rhombus
Square
Kite
Trapezoid
Isosceles
Trapezoid
S
10. Given: STPW is a kite
ST = x + 5
TP = y + 9
SW = 2y +7
WP = 3x – 10
T
W
Find the perimeter of the kite
P
11. Given trapezoid TRAP with TR || AP
T
mA = (12x)°
mP = (300 – 22x)°
mT = (x2)°
Determine mR.
R
(x2)°
P (300 – 22x)°
(12x)°
A
For numbers 12 – 17, write A for always, S for sometimes, or N for never.
12. If two lines are cut by a transversal, alternate exterior angles are congruent.
13. If two parallel lines are cut by a transversal, corresponding angles are congruent.
14. The diagonals of a kite bisect each other.
15. The diagonals of a parallelogram bisect each other.
16. The diagonals of a rectangle are congruent.
17. The diagonals of an isosceles trapezoid bisect each other.
18. Find the perimeter of
a) the isosceles trapezoid.
x+5
(9x + 92)° (32x)°
b) parallelogram ABCD.
D
x
x + 10
(2x + 50)° C
x
3x
A
(4x)°
B
19. A pair of consecutive angles in a rhombus have measures in the ratio of 7 to 5. Find the measure of the smallest angle.
20. One upper base angle and one lower base angle in an isosceles trapezoid are in the ratio of 2 to 7. Find the measure of the largest
angle.
21. ABCD is a kite.
BY = 4x
DY = x + 7.5
AB = 10x + 3
BC = 5x – 4
Find the perimeter.
B
Y
A
D
C
22. List all the possible quadrilateral that satisfy the following statements. Choose from: quadrilateral (Q), parallelogram (P),
Rectangle (Rc), Rhombus (Rh), Square (S), Kite (K), Trapezoid (T), Isosceles Trapezoid (IT)
a) I am a quadrilateral with congruent diagonals.
b) I am a parallelogram with perpendicular diagonals.
c) I am a quadrilateral with diagonals bisected.
d) I am a quadrilateral with two unique pairs of congruent, consecutive sides.
e) I am a parallelogram with congruent, perpendicular diagonals.
f) I am a quadrilateral with one pair of opposite sides parallel.
g) I am a quadrilateral with diagonals perpendicular and bisectors of each other.
h) I am a parallelogram with two pairs of opposite angles bisected by a diagonal.
i) I am a parallelogram with a right angle.
j) I am a rectangle with perpendicular diagonals.
23. In parallelogram ABCD, BC= 9y + 10, AD = 6y + 40, AB =
1
y  50. Find BC, AD, AB, and DC.
2
B
C
24. In parallelogram ABCD, mA = x° and mB = (2x + 60)°. Find the measure of angle A.
For numbers 25 – 38, answer True or False.
25. A parallelogram is a rectangle.
26. A kite is a quadrilateral.
27. An isosceles trapezoid has two congruent legs.
28. A trapezoid has two pairs of opposite sides parallel.
29. A square is kite.
30. If one of the angles of a parallelogram is a right angle, the parallelogram is a square.
31. A rhombus is a square.
32. Diagonals of a rectangle are congruent.
33. Diagonals of a rhombus are congruent.
34. If two parallel lines are cut by a transversal, interior angles on the same side of the transversal are congruent.
35. The diagonals of an isosceles trapezoid bisect each other.
36. In a kite, the diagonals are the perpendicular bisectors of each other.
37. A rectangle is a trapezoid.
38. Diagonals of parallelogram are congruent.
A
E
D
For numbers 39 – 44, write A for always, S for sometimes, or N for never.
39. A rhombus is a square.
40. A square is a rectangle
41. A trapezoid is a parallelogram.
42. A parallelogram is a quadrilateral.
43. The diagonals of an isosceles trapezoid are perpendicular.
44. A square is a rhombus.
45. In rectangle EFGH, mFEG = (4x + 5)° and mGEH = (5x – 14)°. Find mGEH.
E
F
J
46. In rectangle EFGH, EJ = 2x + 3 and FJ = 12 – x. Find FH.
H
47. In square JKLM, mKJL = (9x)°. Find the value x.
48. In square JKLM, JK = x2 – 15 and KL = 2x. Find the perimeter of the square.
49. In rhombus ABCD, mBAE = (x)°, mBEA = (3x)°. Find the mBAD.
G
J
K
M
L
A
B
E
50. In rhombus ABCD, AB = 3x + 4, BC = 7x – 20. Find the perimeter.
51. Find the perimeter of PQRS if PQRS is a kite.
C
D
P
5x – 1
Q
3x
x+4
S
8x + 3
R
52. A pair of consecutive angles of a parallelogram have measures in the ratio of 5 to 4. Find the measure of the larger angle.
53. ARTB is an isosceles trapezoid. Find RC if: AC = x + 5, CT = 2x + 8 and RB = 2x + 17.
A
R
C
B
T