Download Chapters 12-16 Cumulative Test

Chapters 12-16 Cumulative Test
1. True or False
a. SAS, SSS, ASA, and SSA are triangle congruence properties.
b. SAS, SSS, and AA are triangle similarity properties.
c. All squares are congruent to each other.
d. Translations and rotations are the only isometries that do not change the
orientation of a figure.
e. All isometries preserve angle measure.
f. If A' B' is the image of AB under a reflection, then A' B' AB .
2. Sketch the following and include proper labeling to illustrate the size or congruence
of sides and angles.
a. A trapezoid that is not isosceles.
b. A right isosceles triangle.
3. For each of the following name and sketch a type of quadrilateral that has the stated
properties? Sketch the lines of symmetry and/or describe the angles of rotation.
a. Rotational symmetry but not reflexive symmetry
b. Reflexive but not rotational symmetry
c. Neither reflexive nor rotational symmetry
4. a. In the following diagrams let one circle represent the set of acute triangles and the
other circle represent the set of isosceles triangles. Which of the diagrams best
represents the relationship between acute triangles and isosceles?
b. In the following diagrams, let one circle represent the set of kites and the other
circle represent the set of squares. Which of the diagrams best represents the
relationship between kites and squares?
i
ii
iii
5. In the following figure, l m . Given the measures of angles indicated in the figure,
find the measures of the angles identified by a, b, c, d, e, and f.
f
l
e
d
48
m
58
c
a
85
6. The formula for computing the measure of the vertex angle of a regular n-gon can be
(n  2) 180
n  180  360
written as
or
. Select one of the forms of the equation and
n
n
explain how it was derived.
7. The van Hiele levels are levels of reasoning used in learning geometry. Name the first
three van Hiele levels and explain each.
8. Choose the most realistic measures for the following objects. Circle the best answer.
a. The weight of a baseball
b. The height of a desk
c. The volume of a cup of water
10 kg
10 cm
100 kg
1m
200 mL
2 L
100 g
1 km
2 mL
9. Sketch two different rectangles with the same area. What do you notice about their
perimeters? (Be sure to label the dimensions of your rectangles.)
10. Perform each of the following conversions
a. 247 mm2 =
cm2
b. 36 mm =
m
c. 2.39 g
=
mg
d. 108 ft3 =
yd3
e. 247 cm3 =
m3
f. 72 in
yd
=
g. 463 cm3 =
mL
h. 2 gal
=
quarts
11. The number  is equal to 3.14159… What does  represent?
12. Given the top view of a stack of blocks where the numbers tell you how high each
stack of blocks should be.
Which picture below represents the same stack?
13. Find the perimeter of the figure below and leave the answer in exact form.
14. How far will a wheel with radius of
5

feet roll in two revolutions?
15. Explain why the area of the triangle below can be found by using the following
formula.
1
A  bh
2
16. Betty’s yard is shaped as shown in the following figure. If she has a bag of fertilizer
that will cover 450 yd2 of grass, exactly how much of the bag should she spread on
her yard? Justify your answer. (Note: 18’ in the figure means 18 feet.)
17. a. A can of soda has a diameter of 8 cm and a height of 12 cm. What is the volume?
b. What is the volume in milliliters?
c. If 6 cans are packed in a rectangular box so that the cans touch each other and the
sides of the box in a perfect fit, what is the surface area of the box?
18. Explain what in means for two triangles to be congruent by the SAS congruence
property.
B
19. Given that ABCD in the following figure is a parallelogram
A
E
C
D
a. Prove that AED  CED.
b. Use the result of part (a) to show that the diagonals of a parallelogram bisect each
other.
20. a. Use a compass and straightedge to construct the angle bisector of an angle.
b. Explain how the properties of the diagonals of a rhombus are related to the
construction done in part (a).
21. Given the lengths and angles indicated in the following figure, find CE and AD.
E
9
4
A
75 °
C
75 °
6
5
D
22. Given ABC ~ XYZ and
ABC ?
AB
 3 . If the area of XYZ is 8 in2, what is the area of
XY
23. In ABC let l be the perpendicular bisector of side AB and m is the perpendicular
bisector of BC . If l and m intersect at point O, what property does O have in relation
to the vertices of the triangle?
For problems 24-27, let A(0,0), B(5,0), C(8,4), and D(3,4) be the vertices of
quadrilateral ABCD.
24. a. Find the slopes of AB, BC, CD, and DA .
b. Based on the information in part (a), we can conclude ABCD is what type of
quadrilateral?
25. a. Find the lengths of AB, BC, CD, and DA .
b. Based on the information in part (a), we can conclude ABCD is what type of
quadrilateral?
26. a. Find the slopes of diagonals AC and BD .
b. Find the midpoints of AC and BD .
c. Based on parts a. and b. what properties do the diagonals of a rhombus have?
27. Let l be the line that passes through D and is perpendicular to side BC .
a. Find the equation of l.
b. Find the point of intersection of l and BC .
28. Find the following points on the following square lattice.
a. TAB(P)
A
b. RO,-90 (P)
c. MBD (P)
F
d. SE, 3 (P)
B
0
P
E
C
D
29. In each of the following cases, ABC  A' B' C' . Identify the type of isometry that
maps ABC to A' B' C' as either a rotation, translation, reflection, glide reflection or
none and justify your conclusion.
B
B
A
B
A
A
C
C
B'
C
C'
C'
A'
B'
A'
A'
C'
B'
a.
b.
c.