WGU D128 OBJECTIVE ASSESSMENT
MATHEMATICS FOR ELEMENTARY
EDUCATORS EXAM: (LATEST 2026/2027
UPDATE), WITH CORRECT/ACCURATE
ANSWERS
WGU D128 OBJECTIVE ASSESSMENT
MATHEMATICS FOR ELEMENTARY
EDUCATORS
Questions 1–25
1. Which similarity theorem can be used to prove that two figures are similar but not necessarily
congruent?
A. Side-Side-Side (SSS)
B. Side-Angle-Side (SAS)
C. Angle-Angle (AA)
D. Hypotenuse-Leg (HL)
Correct Answer: C. Angle-Angle (AA)
Rationale: The Angle-Angle similarity theorem states that if two angles of one triangle are congruent to two
angles of another triangle, the triangles are similar. Similar figures have the same shape but may differ in
size, which distinguishes similarity from congruence. Congruence requires all corresponding sides and
angles to be equal, while similarity does not. Therefore, AA proves similarity without guaranteeing
congruence.
2. Which transformation maps the point (2, 5) onto the point (−2, 5)?
A. (x, −y)
B. (−x, y)
C. (x + 4, y)
D. (x, y − 5)
Correct Answer: B. (−x, y)
Rationale: The transformation (−x, y) reflects a point across the y-axis. Applying this rule to the point (2, 5)
,changes the x-coordinate to −2 while keeping the y-coordinate the same. This results exactly in the point (−2,
5). Therefore, the transformation is a reflection across the y-axis.
3. Two triangles are drawn on a coordinate plane. The first triangle has vertices at (5, 4), (−4, 6), and
(−8, 9). The second triangle has vertices at (1, 6), (−8, 8), and (x, y). What ordered pair allows the
triangles to be congruent?
A. (−10, 9)
B. (−12, 11)
C. (−11, 10)
D. (−9, 12)
Correct Answer: B. (−12, 11)
Rationale: Congruent triangles must have equal corresponding side lengths and angles. By comparing the
translation pattern between the known points of the two triangles, the same vector can be applied to
determine the missing vertex. Applying this consistent transformation results in the point (−12, 11). This
ensures all corresponding vertices align correctly, confirming congruence.
4. An octagon in the coordinate plane undergoes a transformation. Which transformation would result
in a figure that is similar to the original?
A. (x + 5, y + 5)
B. (−x, y)
C. (5x, 5y)
D. (x − 3, y − 3)
Correct Answer: C. (5x, 5y)
Rationale: A dilation multiplies all coordinates by a constant scale factor. The transformation (5x, 5y)
enlarges the figure while preserving its shape and angle measures. Similar figures have proportional side
lengths and identical angles. Translations and reflections preserve congruence, not similarity through
resizing.
5. The figures shown undergo a transformation in which all dimensions are proportionally increased.
What type of transformation is this?
A. Translation
B. Reflection
C. Rotation
D. Dilation
Correct Answer: D. Dilation
Rationale: A dilation changes the size of a figure while maintaining its shape. All distances from the center
of dilation are multiplied by the same scale factor. This results in similar figures rather than congruent ones.
Translations, reflections, and rotations preserve size and produce congruent figures.
, 6. A circle has an area of approximately 615.75 square inches. What is the approximate circumference
of the circle?
A. 43.98 in
B. 62.80 in
C. 87.96 in
D. 123.10 in
Correct Answer: C. 87.96 in
Rationale: The area of a circle is given by the formula A = πr². Solving for the radius using the given area
yields a radius of approximately 14 inches. The circumference is calculated using C = 2πr, which results in
approximately 87.96 inches. This value best matches the correct choice.
7. What is the area of the figure shown if it is composed of rectangles and triangles with known
dimensions?
A. 48 square units
B. 56 square units
C. 63 square units
D. 72 square units
Correct Answer: C. 63 square units
Rationale: The area of a composite figure is found by dividing it into simpler shapes. Each individual area is
calculated separately and then added together. Performing these calculations results in a total area of 63
square units. This method ensures accuracy when working with irregular shapes.
8. A triangular window has an area of 600 square inches. If the base of the triangle is three times the
height, what is the length of the base?
A. 20 in
B. 40 in
C. 60 in
D. 80 in
Correct Answer: C. 60 in
Rationale: The area of a triangle is given by A = ½bh. Since the base is three times the height, substitute b =
3h into the formula. Solving the equation yields a height of 20 inches and a base of 60 inches. This satisfies
both the area and proportional conditions.
9. A rectangular garden has an area of 374 square yards and a length of 17 yards. If the width is
doubled, how much fencing is needed to enclose the new garden?
A. 94 yd
B. 108 yd
C. 122 yd
D. 136 yd
MATHEMATICS FOR ELEMENTARY
EDUCATORS EXAM: (LATEST 2026/2027
UPDATE), WITH CORRECT/ACCURATE
ANSWERS
WGU D128 OBJECTIVE ASSESSMENT
MATHEMATICS FOR ELEMENTARY
EDUCATORS
Questions 1–25
1. Which similarity theorem can be used to prove that two figures are similar but not necessarily
congruent?
A. Side-Side-Side (SSS)
B. Side-Angle-Side (SAS)
C. Angle-Angle (AA)
D. Hypotenuse-Leg (HL)
Correct Answer: C. Angle-Angle (AA)
Rationale: The Angle-Angle similarity theorem states that if two angles of one triangle are congruent to two
angles of another triangle, the triangles are similar. Similar figures have the same shape but may differ in
size, which distinguishes similarity from congruence. Congruence requires all corresponding sides and
angles to be equal, while similarity does not. Therefore, AA proves similarity without guaranteeing
congruence.
2. Which transformation maps the point (2, 5) onto the point (−2, 5)?
A. (x, −y)
B. (−x, y)
C. (x + 4, y)
D. (x, y − 5)
Correct Answer: B. (−x, y)
Rationale: The transformation (−x, y) reflects a point across the y-axis. Applying this rule to the point (2, 5)
,changes the x-coordinate to −2 while keeping the y-coordinate the same. This results exactly in the point (−2,
5). Therefore, the transformation is a reflection across the y-axis.
3. Two triangles are drawn on a coordinate plane. The first triangle has vertices at (5, 4), (−4, 6), and
(−8, 9). The second triangle has vertices at (1, 6), (−8, 8), and (x, y). What ordered pair allows the
triangles to be congruent?
A. (−10, 9)
B. (−12, 11)
C. (−11, 10)
D. (−9, 12)
Correct Answer: B. (−12, 11)
Rationale: Congruent triangles must have equal corresponding side lengths and angles. By comparing the
translation pattern between the known points of the two triangles, the same vector can be applied to
determine the missing vertex. Applying this consistent transformation results in the point (−12, 11). This
ensures all corresponding vertices align correctly, confirming congruence.
4. An octagon in the coordinate plane undergoes a transformation. Which transformation would result
in a figure that is similar to the original?
A. (x + 5, y + 5)
B. (−x, y)
C. (5x, 5y)
D. (x − 3, y − 3)
Correct Answer: C. (5x, 5y)
Rationale: A dilation multiplies all coordinates by a constant scale factor. The transformation (5x, 5y)
enlarges the figure while preserving its shape and angle measures. Similar figures have proportional side
lengths and identical angles. Translations and reflections preserve congruence, not similarity through
resizing.
5. The figures shown undergo a transformation in which all dimensions are proportionally increased.
What type of transformation is this?
A. Translation
B. Reflection
C. Rotation
D. Dilation
Correct Answer: D. Dilation
Rationale: A dilation changes the size of a figure while maintaining its shape. All distances from the center
of dilation are multiplied by the same scale factor. This results in similar figures rather than congruent ones.
Translations, reflections, and rotations preserve size and produce congruent figures.
, 6. A circle has an area of approximately 615.75 square inches. What is the approximate circumference
of the circle?
A. 43.98 in
B. 62.80 in
C. 87.96 in
D. 123.10 in
Correct Answer: C. 87.96 in
Rationale: The area of a circle is given by the formula A = πr². Solving for the radius using the given area
yields a radius of approximately 14 inches. The circumference is calculated using C = 2πr, which results in
approximately 87.96 inches. This value best matches the correct choice.
7. What is the area of the figure shown if it is composed of rectangles and triangles with known
dimensions?
A. 48 square units
B. 56 square units
C. 63 square units
D. 72 square units
Correct Answer: C. 63 square units
Rationale: The area of a composite figure is found by dividing it into simpler shapes. Each individual area is
calculated separately and then added together. Performing these calculations results in a total area of 63
square units. This method ensures accuracy when working with irregular shapes.
8. A triangular window has an area of 600 square inches. If the base of the triangle is three times the
height, what is the length of the base?
A. 20 in
B. 40 in
C. 60 in
D. 80 in
Correct Answer: C. 60 in
Rationale: The area of a triangle is given by A = ½bh. Since the base is three times the height, substitute b =
3h into the formula. Solving the equation yields a height of 20 inches and a base of 60 inches. This satisfies
both the area and proportional conditions.
9. A rectangular garden has an area of 374 square yards and a length of 17 yards. If the width is
doubled, how much fencing is needed to enclose the new garden?
A. 94 yd
B. 108 yd
C. 122 yd
D. 136 yd
