Chapter 13 Test Review Complete your work on your own paper.
1. Analyze parallelogram ABCD.
a. Rotate parallelogram ABCD about the origin 90°
counterclockwise. Graph and label the image as A’B’C’D’. Identify
the vertex coordinates of image A’B’C’D’.
A’ (-4, 4)
B’ (-1, 3)
C’ (-1, 7)
D’ (-4, 8)
b. Rotate parallelogram ABCD about the origin 180°
counterclockwise. Graph and label the image as A’B’C’D’.
Identify the vertex coordinates of image A’B’C’D’.
A’: (-4, -4)
B’ (-3, -1)
C’ (-7, -1)
D’ (-8, -4)
2. Analyze the two triangles shown.
a. Determine the transformation used to create triangle STU.
A reflection over the x-axis
b. Write a triangle congruence statement for the triangles shown.
⊿𝑀𝑁𝑂 ≅ ⊿𝑆𝑇𝑈
c. Identify the congruent angles and congruent sides of the triangles.
∠𝑀 ≅ ∠𝑆
∠𝑁 ≅ ∠𝑇
∠𝑂 ≅ ∠𝑈
̅̅̅
̅̅̅̅̅
𝑀𝑁 ≅ ̅𝑆𝑇
̅̅̅̅
̅̅̅̅
𝑁𝑂 ≅ 𝑇𝑈
̅̅̅̅̅
𝑀𝑂 ≅ ̅̅̅̅
𝑆𝑈
3. Refer to the figure at the right.
a. What are the coordinates of each vertex if the figure is rotated 90°
counterclockwise about the origin?
A’ (-2, -2) B’ (-5, 2) C’ ( -3, 6) D’ (3, 4)
b. What are the coordinates of each vertex if the figure is rotated 180°
counterclockwise about the origin?
A’ (2, -2) B’( -2, -5) C’ ( -6, -3) D’ (-4, 3)
c. What are the coordinates of each vertex if the figure is rotated 270° counterclockwise about the origin?
A’ (2, 2) B’ (5, -2) C’ ( 3, -6) D’ (-3, -4)
d. What are the coordinates of each vertex if the figure is rotated 90° clockwise about the origin?
A’ (2, 2) B’ (5, -2) C’ ( 3, -6) D’ (-3, -4)
4. A triangle has vertices at F (-7, 3), G (2, 6), and H (3, 5). What are the coordinates of each vertex if the triangle is
a. Reflected over the x axis?
F’ (-7, -3), G’(2, -6), H’(3, -5) - The y-values change signs.
b. Reflected over the y axis?
F’(7, 3), G’(-2, 6) H’(-3, 5) - The x-values change signs.
c. Reflected over the x axis then the y axis?
F’(7, -3), G’(-2, -6) H’(-3, -5)
d. Rotated 180°?
F’(7, -3), G’(-2, -6) H’(-3, -5)
e. Translated 9 units to the right?
i. F’(2, 3), G’ (11, 6), H’ (12, 5)
f.
Translated 2 units up?
F’(-7, 5), G’ (2, 8), H’ (3, 7)
g. Translated 3 units up and 1 unit left?
F’ (-8, 6), G’ (1, 9), and H’ (2, 8)
5. A triangle has vertices at A(-3, -1), B(-6, -5), C( -1, -4). Which transformation would produce an image with
a. Vertices at A’(1, -3), B’(5, -6), C’ (4, -1)?
A rotation 90° counterclockwise
b. Vertices at A’(3, -1), B’(6, -5), C’( 1, -4)?
A reflection over the y-axis
c. Vertices at A’(-3, 4), B’(-6, 0), C’( -1, 1)?
A vertical shift up five units
6. Write a triangle congruence statement that applies to this figure.
a. ⊿𝐺𝑁𝑅 ≅ ⊿𝑊𝐾𝐹
7. Is it possible to show that the following triangles are congruent? IF so,
state the theorem you would use.
Yes; ASA
No
Yes; ASA
Yes; SAS
Yes; ASA
Yes; AAS