Assessment Bank: Linear Algebra Focus 1-3
Note: This is not a unit test. These are items aligned to the 3 on the learning
scale for the unit(s).
1) Given the two congruent triangles below, describe a sequence of transformations that would
“move” one triangle exactly onto the other. Be sure to include any reflections, centers and
angles of rotation, and directions and distances of translations. (8.G.A.1)
2) Provide the minimum amount of information needed to guarantee that these two triangles
are congruent. (Note: The information needed is a list of measurements.) (8.G.A.2)
3) Under a particular transformation, point A’ is the image of point A and point B’ is the image
of point B.
a) Give a detailed description of the transformation. (8.G.A.1)
b) Use a ruler and an angle ruler or protractor to help you draw the image of trapezoid
ABCD under the transformation you described in part (a). (8.G.A.1)
c) Are the pre-image and the image congruent? Explain why or why not. (8.G.A.2)
4) The large triangle below is made from congruent triangles.
a) If you moved Triangle 1 onto Triangle 2, which vertices would match? (8.G.A.1)
b) Carefully describe a combination of transformations that would move Triangle 1 onto
Triangle 2. You may add lines or points to the diagram. (8.G.A.2)
5) Use the graph below.
a) Describe a sequence of reflections that transforms ABCD to image A’B’C’D’ (8.G.A.2)
b) Describe a rotation that transforms ABCD to image A’B’C’D’ (8.G.A.2)
c) Describe how the rotation in part (b) affects the coordinates of vertices A, B, C, D
(8.G.A.3)
6) The diagram below shows PQRS on a coordinate plane. Justify how PQRS was transformed to
P’Q’R’S’ (8.G.A.3)
7) The diagram below shows PQRS on a coordinate plane. Justify how PQRS was transformed to
P’Q’R’S’ (8.G.A.3)
8) The diagram below shows PQRS on a coordinate plane. Justify how PQRS was transformed to
P’Q’R’S’ (8.G.A.3)
9) The diagram below shows PQRS on a coordinate plane. Justify how PQRS was transformed to
P’Q’R’S’ (8.G.A.3)
10)Three triangles are graphed on the coordinate grid. Show evidence that Triangle 1 and
Triangle 2 are congruent by finding one or more transformations that would move Triangle
1 to the exact position of Triangle 2. Give complete descriptions of these transformations.
(8.G.A.3)
11. Find the measure of each angle in the diagram below.
BAC ______
ACB ______
Directions: In diagram below line x is parallel to line y. Use
the diagram to answer questions 2 through 6.
12. Name a pair of alternate interior angles.
13. Name a pair of corresponding angles.
14. Name a pair of alternate exterior angles.
15. Find the measure of each angle in the diagram.
a ______
f______
b ______
g ______
n ______ p ______
c ______
d ______
e ______
h ______
k ______
m ______
r ______
t ______
v ______
16. Explain how you found the measure of m.
Jack drew the triangle to the right in the Match Game.
17. Which measurements of angles and sides can he give
partner to ensure that she draws a congruent triangle?
his
18. What two measurements can he give his partner to ensure that she draws a similar
triangle?
Directions: In diagram below PQ is parallel to RS. Use the diagram to answer questions 19
and 20.
19. Name another angle whose measure is 76˚.
20. Explain how you know this angle has the same measure.
21. Look at the figure on the
coordinate grid. On the same
coordinate grid, draw a figure
similar but NOT congruent to the
provided.
that is
figure
22. Show that triangles 1 and 2 are congruent by finding one
or more transformations that would move triangle 1 to the
exact position of triangle 2. Give a complete description of
these transformations.
Directions: Use the following diagram and information for
questions 23 through 24.
23. Is triangle 1 similar to triangle 3? ______
If so, how can you tell? _________________
___________________________________
___________________________________
24. What is the scale factor? _____________
Directions: Use the following diagram and information for questions 25 through 28.
An engineer decides to use similar
triangles to find the distance across the
river. He makes the diagram shown.
25. Which triangles appear to be similar?
B
current
bridge
new
bridge
A
26. What must the engineer know about
these triangles to conclude they are
similar?
200 ft.
C
250 ft.
150 ft.
E
400 ft.
D
27. Find the distance across the river from point B to point A. Explain how you found your
answer.
28. Why does BC have the same slope as CD?