1. What term describes a transformation that does not change a figure’s size or shape?

(A) similarity

(B) isometry

(C) collinearity

(D) symmetry

For questions 2–4, use the diagram showing parallelogram ABCD.

  1. A reflection across carries parallelogram ABCD onto itself.

(A) True

(B) False

  1. A rotation of 90° about I carries parallelogram ABCD onto itself.

(A) True

(B) False

  1. A rotation of 180° about I carries parallelogram ABCD onto itself.

(A) True

(B) False

  1. Which of these is equivalent to a translation?

(A) a reflection across one line

(B) a composition of two reflections across intersecting lines

(C) a composition of two reflections across parallel lines

  1. A regular polygon with n sides is carried onto itself by a positive rotation about its center that is a multiple of 60°, but less than 360°.

Which could NOT be the value of n?

(A) 3

(B) 4

(C) 5

(D) 6

  1. In the diagram, and B lies on line g.

The figure ABC is reflected across line g, and its image is reflected across line h. What is the distance from line g to the final image of point A?

(A) 5 cm

(B) 15 cm

(C) 20 cm

(D) 25 cm

  1. What is the image of the point (–4, 6) under the transformation ?

(A) (6, 4)

(B) (–6, –4)

(C) (4, 6)

(D) (–4, –6)

  1. A figure is rotated about the origin by 180°, then is translated 4 units right and one unit up. Which describes the results of the two transformations?

(A)

(B)

(C)

(D)

  1. The point A(4, 3) is rotated –90° about the origin. In which quadrant is A' ?

(A) I

(B) II

(C) III

(D) IV

  1. A figure is reflected across the line y = 2, then reflected across the line y = 4. Which single transformation results in the same image?

(A) a reflection across the line y = 3

(B) a reflection across the line y = 6

(C) a translation 2 units up

(D) a translation 4 units up

  1. Point is the image of point A under a transformation T. Line  is the perpendicular bisector of at point M. Which describes the transformation T?

(A) a reflection across 

(B) a 90° rotation about M

(C) a translation by the vector from A to M

(D) a dilation about M with scale factor 2

For questions 13–16, determine if the described transformation(s) is/are an isometry.

  1. A reflection is an isometry.

(A) True

(B) False

  1. A composition of two reflections is an isometry.

(A) True

(B) False

  1. A dilation is an isometry.

(A) True

(B) False

  1. A composition of a rotation and a dilation is an isometry.

(A) True

(B) False

  1. In , M is the midpoint of and N is the midpoint of . For which type of triangle is ?

(A) equilateral only

(B) isosceles only

(C) scalene only

(D) any triangle

  1. After a figure is rotated, . Which statement(s) could be true?

(A) The center of rotation is P.

(B) The angle of rotation is a multiple of 360°.

(C) Either A or B or both.

(D) Neither A nor B.

  1. Use the diagram.

Which series of reflections would result in a rotation of –44° about A?

(A) reflect across k¸ then reflect across 

(B) reflect across ¸ then reflect across k

(C) reflect across ¸ then reflect across m

(D) reflect across m¸ then reflect across 

For questions 20–21, a transformation S is defined as .

  1. The pre-image of under S is .

(A) True

(B) False

  1. S is an isometry.

(A) True

(B) False

  1. Which transformation does NOT preserve the orientation of a figure?

(A) dilation

(B) reflection

(C) rotation

(D) translation

  1. Given point A is located at (1, 3). What is the final image of A after this series of transformations?

(1) Reflect A across the y axis.
(2) Translate the image such that .

(A) (–1, –3)

(B) (–3, 5)

(C) (–3, –1)

(D) (–5, 5)

For questions 24–27, use the diagram where B is the reflection of A across .

  1. PA = PB

(A) True

(B) False

(A) True

(B) False

  1. AQ = QB

(A) True

(B) False

(A) True

(B) False

  1. Use the figure.

A transformation T is defined as . Which shows the image of figure under T?

(A)

(B)

(C)

For questions 29–31, use the diagram where ABCD is a quadrilateral with and . Diagonals and intersect at E.

(A) True

(B) False

(A) True

(B) False

(A) True

(B) False

  1. A figure is transformed in the plane such that no point maps to itself. What type of transformation must this be?

(A) dilation

(B) reflection

(C) rotation

(D) translation

For questions 33–36, determine if the mapping is an isometry.

  1. is an isometry.

(A) True

(B) False

  1. is an isometry.

(A) True

(B) False

  1. is an isometry.

(A) True

(B) False

  1. is an isometry.

(A) True

(B) False

For questions 37–38, determine the truth of the statements about rotations.

  1. Rotations preserve the orientation of a figure.

(A) True

(B) False

  1. Under a rotation, no point can map to itself.

(A) True

(B) False

For questions 39–41, point P is located at (6, 0) and undergoes a transformation.

  1. A rotation of 90° about P results in P = P.

(A) True

(B) False

  1. A translation by the vector results in P = P.

(A) True

(B) False

  1. A reflection about the x axis results in P = P.

(A) True

(B) False

For questions 42–43, use the diagram which shows ABC has been reflected across an unknown line , then reflected across line m to produce ABC.

  1. The equation of line  is x = –0.5.

(A) True

(B) False

  1. If ABC were reflected across line m first, then reflected across line to produce ABC, the equation of line  would be x = –0.5.

(A) True

(B) False

For questions 44–46, consider a triangle that has been transformed through rigid motions and its image compared to . Determine if the given information is sufficient to draw the provided conclusion.

/ Given / Conclusion

(A) True

(B) False

/ Given / Conclusion

(A) True

(B) False

/ Given / Conclusion

(A) True

(B) False

  1. Use the diagram.

Which statement would be used to prove lines r and s are parallel?

(A) and are congruent

(B) and are complementary

(C) and are congruent

(D) and are supplementary

Look at the figure below.

Look at these three figures.

  1. Which figures are congruent to the first figure?

(A) I only

(B) II only

(C) I and II only

(D) I, II, and III

For questions 49–50, consider where AB = BC and .

(A) True

(B) False

(A) True

(B) False

For questions 51–53, evaluate whether the image of a figure under the described transformation is congruent to the figure.

  1. A transformation T follows the rule . The image of a figure under T is congruent to the figure.

(A) True

(B) False

  1. A transformation T follows the rule . The image of a figure under T is congruent to the figure.

(A) True

(B) False

  1. A transformation T follows the rule . The image of a figure under T is congruent to the figure.

(A) True

(B) False

In the diagram, and .

  1. What is the value of x?

(A) 44

(B) 88

(C) 92

(D) 176

Use the Venn diagram.

  1. A quadrilateral ABCD has 4 lines of symmetry. Identify the area of the diagram in which ABCD resides.

(A) III

(B) IV

(C) V

(D) VII

  1. Right triangle PQR has sides of length 6 units, 8 units, and 10 units. The triangle is dilated by a scale factor of 4 about point Q. What is the area of triangle P'Q'R'?

(A) 96 square units

(B) 192 square units

(C) 384 square units

(D) 768 square units

  1. The ratio of the side lengths of a triangle is 3:6:8. A second triangle is similar to the first and its shortest side measures 8.0 centimeters. What is the length of the longest side of the second triangle?

(A) 3.0 cm

(B) 10.7 cm

(C) 13.0 cm

(D) 21.3 cm

Use the diagram below.

  1. What is the value of y?

(A) 13

(B) 18

(C) 27

In the diagram, a student has placed a mirror on level ground, then stands so that the top of a nearby tree is visible in the mirror.

  1. What is the height of the tree?

(A) 24 m (B) 35 m

(B) 41 m(D) 59 m

In the diagram, .

  1. What is the value of x?

(A) 11

(B) 6

(C) 5

(D) 3

  1. Which figure contains two similar triangles that are NOT congruent?

(A)

(B)

(C)

(D)

  1. Sally constructs a triangle where two of the angles measure 50° and 60°. Tom constructs a triangle where two of the angles measure 50° and 70°. What is true about the two triangles?

(A) The triangles cannot be similar.

(B) The triangles could be similar.

(C) The triangles must be similar.

  1. Triangle ABC has vertices , , and . The triangle is dilated about the point with scale factor 4. What is the location of A' ?

(A)

(B)

(C)

(D)

Use the diagram.

  1. Dilate line m about the origin with scale factor 2. What is the equation of the line’s image?

(A) y = 2x + 2

(B) y = 2x + 4

(C) y = 4x + 2

(D) y = 4x + 4

  1. Which is NOT a criterion for triangle similarity?

(A) angle-angle

(B) angle-side-angle

(C) side-angle-side

(D) side-side

  1. J(5, 7) is the image of J(3, 3) after a dilation with scale factor 3. Where is the center of dilation?

(A) (–3, –9)

(B) (0, 0)

(C) (2, 1)

(D) (4, 5)

In the diagram, segments and intersect at E, F lies on , and .

  1. The two segments are dilated about F with scale factor . What is ?

(A) 30°

(B) 60°

(C) 90°

(D) 120°

  1. In the diagram, ABCD is dilated with center O to produce A'B'C'D', and .

What is ?

(A) (B)

(C) 2(D) 3

  1. Use the diagram.

Which is equal to h?

(A)

(B)

(C)

(D)

  1. J(5, 7) is the image of J(3, 3) after a dilation with scale factor 3. Where is the center of dilation?

(A) (–3, –9)

(B) (0, 0)

(C) (2, 1)

(D) (4, 5)

  1. Fred stands at corner A of a rectangular field shown below. He needs to get to corner C.

What is the shortest distance from A to C?

(A) 9 m(B) 13 m

(C) 15 m (D) 21 m

Use the right triangle. What is the value of x?

  1. What is the value of x?

(A)

(B)

(C) 7

(D) 17

  1. Consider a triangle ABC. Which statement is true?

(A)

(B)

(C)

(D)

  1. Use the diagram.

What is ?

(A) (B)

(C) (D)

  1. A small airplane flies due north at 150 kilometers per hour. A wind is blowing towards the direction 60° east of north at 50 kilometers per hour. Which figure represents the final speed and direction of the airplane?

(A) (B) (C) (D)

For questions76-78, consider a triangle ABC and each given set of measurements.

  1. AB, AC, and are sufficient to solve the triangle using the Law of Sines.

(A) True

(B) False

  1. AB, AC, and are sufficient to solve the triangle using the Law of Sines.

(A) True

(B) False

  1. AB, AC, and BC are sufficient to solve the triangle using the Law of Sines.

(A) True

(B) False

  1. The diagram shows a parallelogram ABCD.

What is the parallelogram’s area?

(A)

(B)

(C)

(D)

  1. In the diagram, is a non-right triangle.

Which describes the area of the triangle?

(A)

(B)

(C)

(D)

  1. Given: and

What is the approximate value of ?

(A) –0.90

(B) –0.44

(C) 0.44

(D) 0.90

For questions 82-84, use the statement below.

Given: An angle measures k°, where k > 0.

(A) True

(B) False

(A) True

(B) False

(A) True

(B) False

  1. Let . What is the value of ?

(A)

(B) 1 – m

(C)

(D)

  1. In , C is a right angle, . What is cos B?

(A)

(B)

(C)

(D)

  1. Use the diagram.

Which statement is true?

(A)

(B)

(C)

  1. Use the diagram.

Which is the value of x?

(A)

(B)

(C)

(D)

  1. Use the diagram.

What is the value of d ?

(A) 5

(B)

(C) 10

(D)

For questions 90-92, let .

  1. = m

(A) True

(B) False

  1. = m

(A) True

(B) False

  1. = m

(A) True

(B) False

  1. Let . Which statement is true?

(A)

(B)

(C)

(D)

  1. What is ?

(A) 30°

(B) 45°

(C) 60°

(D) 90°

  1. In the diagram, BC < BD and BD = AD.

Which statement is true?

(A)

(B)

(C)


  1. What is tan 60°?

(A)

(B)

(C)

(D)

  1. What is ?

(A) 30°

(B) 45°

(C) 60°

(D) 90°

  1. In , the sine of angle G equals . is a dilation of about G with a scale factor of 2. What is the sine of angle G' ?

(A)

(B)

(C)

(D) 1