CP Geometry Graded Assignment
Name: _____________________________________________
For each problem all work must be show for full credit.
1.
A
In trapezoid ABCD, L and M are midpoints. Find x and AB, and CD. Write the property of trapezoids that you
used.
3x – 1
L
D
B
3x + 1
M
5x – 5
C
2. In trapezoid QRST, L and M are midpoints , Find x and QR,ST, LM. Write the property of trapezoids that you used.
Q
x2 – 4x + 10
L
x+2
M
T
x
S
R
3. In isosceles trapezoid , Find x and y. Write the property of trapezoids that you used.
M
15x + 12y
S 10 x + 4y
120
E
60
T
4. Using the figure to the right, complete the following.
B
Name all non-consecutive vertices to F
A
D
Name both consecutive sides to AB
E
Name all non consecutive sides to AE
Name all non consecutive vertices to A
How many total diagonals can be drawn in the figure? Show formula and work
5. Draw a concave octagon.
6. Draw a regular quadrilateral
Describe/circle the part that makes it concave.
Describe what makes it regular.
F
7. Find the number of diagonals of each convex polygon. Show your work
18-gon
nonagon
8. The measure of one interior angle of a regular polygon is 3 times the measure of one exterior angle of the regular
polygon, find the measure of the interior angle and the exterior angle. How many sides does the polygon have?
9. A regular polygon has 10 sides. Find the measure of one exterior angle and the measure of one interior angle.
Show all work.
10. If the measure of one exterior angle of a regular polygon is 60o. How many sides does the figure have? Show all
work.
11. The sum of the measures of 4 interior angles of an hexagon is 590 ᵒ. One of the remaining angles is 10ᵒ larger
than the other remaining angle. What is the measure of each of these angles
12. The measurements of the exterior angles of a pentagon are x+ 10, x – 1, 3x + 12, 2x + 8 and 5x – 5. Draw a
diagram to illustrate the problem. Find x. Show all work.
13. Place a checkmark in each box where the property applies.
Property
Opposite sides //
Parallelogram
Square
Rectangle
Rhombus
Opposite sides =
Opposite angles =
One diagonal forms 2 = Δ
Diagonals bisect each other
Diagonals are =
Diagonals bisect angles
All angles are 90º
All sides are =
Diagonals are perpendicular
For each problem list a reason for writing the equation. Solve the equation for x. Answer any additional questions stated
within the problem.
Problem
14. Given Parallelogram ABCD with
AB = 2x + 5 and CD = 3(x – 1) . Find x ,AB
A
B
D
C
15. Given Parallelogram ABCD with
<D = 3x - 40 and < A = 2x – 30. Find x ,<A, < B
A
B
D
C
Reason/ Solution
16.
Given Rectangle ABCD with
AB =3x + 1, CD = 4x – 5 , AD =3(y + 5 ),
BC = 21 Find x , y and perimeter of ABCD
A
B
D
17.
C
Given Parallelogram ABCD with
AM =4x + 3, AC = 5x – 4 Find x and AM
A
B
M
D
18.
C
Given Rhombus ABCD with
<MAB =5x + 38 and < MBA = 8x Find x
A
B
M
D
C
19.
Given Rectangle METS
MT = x2 – 4x – 2 , ES =2 x + 5 . Find x and MC
M
E
C
S
T
20.
Given Rhombus ABCD with
<CAB = 3x – 10 and <DAC = 2x + 14 , Solve for x and
Find <DAB
A
B
D
C
21. Given Parallelogram METS
<ETS = 10(x + 6) and < SME 12x + 42 Find x and <
MET
M
E
S
T
22.
Given Rhombus ABCD with
AB = 10 and BD = 16. What is AM?
A
B
M
D
C