Complete each statement. Do not use square as an answer. 1. The three midsegments of a triangle divide the triangle into ____________________ . 2. The opposite angles of a parallelogram are ________________________ . 3. Each interior angle of a regular octagon measures _____________________ . 4. The length of a midsegment of a trapezoid is the _______________________ of the lengths of the bases. 5. The nonvertex angles of a kite are ______________________________. 6. The consecutive angles of a parallelogram are ___________________________ . 7. An equilateral quadrilateral is usually called a _______________________ . 8. The diagonals of a ________________________ are perpendicular bisectors of each other. 9. The diagonals of a parallelogram ____________________________ each other. 10. The sum of the measures of the angles of a heptagon is _______________________ . 11. The midsegment of a trapezoid is _______________________ to the two bases. 12. The vertex angles of a kite are _________________________ by the diagonal. 13. The diagonals of a ________________________ are equal in length. 14. In an isosceles trapezoid, the base angles are ____________________________ . 15. The length of a midsegment between two sides of a triangle is ___________________ the length of the third side.
82º
Find each lettered angle measure. 16.
90º
a = _________
17.
b = _________
18.
c = _________
19.
d = _________
20.
e = _________
21.
f = _________
22.
g = _________
23.
h = _________
d
40º e
b f
70º
g
c
76º h
a
56º
Find each lettered measure. 24.
a = _________
25.
x = _________
26.
y = _________
27.
a = _________
28.
b = _________
29.
x = _________
30.
y = _________
x
Perimeter = 64 26º
y 12
a
96º
a 46º
y
28
b x 24 a
31.
a = _________
32.
w = _________
33.
x = _________
34.
y = _________
x 21
58º
y w 70º
32
A regular octagonal mirror frame is to be build from strips of 2-inch-wide pine lattice. At what angles a and b should the lattice be cut? 35.
a = _________
36.
b = _________ b
b
a a
37. In triangle RNT, RZ is a median, NZ is equal to 5x - 8, and ZT is equal to 7x - 18. What is the length of NT (in inches)? R
N
Z
T
38. A midsegment of trapezoid TRSK measures 52.5 mm. The longer base is 64.3 mm. T
K What is the length of the shorter base?
R
S
Provide each missing reason or statement in this flowchart proof. Given: Isoseles Trapezoid LMNP, with LM ˜= PN and diagonals LN and PM Show: LN = ˜ PM Given L
LMNP is an isosceles trapezoid
P
Def. of isosceles trapezoid LM ˜= PN Base ∠s of Isosceles Trap ˜= 39. ______________
M
N
42. _____________
44. ______________
43. ______________
45. ______________
40. __________________ 41. _______________
46. Find the measure of the sum of the interior angles of a regular heptagon, and the measure of one exterior angle of a regular heptagon.
The quadrilateral below is a rhombus, and the measure of ∠NML = 21º. J
K
N
M
L
47. What is the measure of ∠JNK?
48. What is the measure of ∠JKL?
49. What is the measure of ∠KJN?
50. In the figure below, ∆FIG is congruent to ∆HGI. What is the measure of ∠HGI? G
H (5x)º
(2x)º 40º F
I
51. M, S, and R are midpoints of the sides of triangle NTQ. MR = 31 cm, SR = 24 cm, and TQ = 70 cm. Find the perimeter of triangle NTQ and the perimeter of triangle MSR. N
S
M 31 cm
T
24 cm
R
Q
70 cm
52. Given m∠IPT = 6x - 12 and KP = 4x, find KT. I
K
4x
(6x - 12)º P
E
T
53. ABCD is an isosceles trapezoid with BE = x + 5, CE = y - 2, AE = x + 1, BD = y + 2. Find AC. A
D E
B
C
RHOM is a rhombus O (?, ?)
y H (9, 13)
M (14, 8) R (4, 3) x 54. Find the coordinates of point O.
55. Find the slopes of HM and RO.
56. What does the result in the previous problem verify.
What is the most descriptive name for each quadrilateral below. 57. _________________
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