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Geometry (Grades 9–10) Midterm — Semester 2, Form A

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Math Grades 9–10 15 multiple choice + 1 written

Free printable Geometry midterm (Grades 9–10): 15 multiple-choice questions plus 1 written response covering Congruence & Similarity, Right Triangles & Trigonometry, Circles, Area & Volume. Answer key included — customize it in the Midterm Maker.

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Geometry (Grades 9–10) Midterm — Semester 2, Form A
Name: Date: Period:

Directions: Read each question carefully and choose the best answer. Answer the written response in complete sentences.

Covers: Congruence & Similarity · Right Triangles & Trigonometry · Circles, Area & Volume

Part 1: Multiple Choice

  1. Which transformation produces a figure that is similar but NOT congruent to the original?
    1. A. A dilation with scale factor 3
    2. B. A reflection over the y-axis
    3. C. A translation 5 units up
    4. D. A rotation of 90°
  2. Two similar rectangles have perimeters in the ratio 2:5. What is the ratio of their areas?
    1. A. 4:10
    2. B. 8:125
    3. C. 2:5
    4. D. 4:25
  3. In triangles PQR and XYZ, ∠P ≅ ∠X, side PQ ≅ side XY, and ∠Q ≅ ∠Y. Which postulate proves the triangles congruent?
    1. A. SSS
    2. B. HL
    3. C. SAS
    4. D. ASA
  4. What does CPCTC stand for?
    1. A. Corresponding points of congruent triangles are collinear
    2. B. Congruent parallel chords to a circle
    3. C. Congruent parts of corresponding triangles are complementary
    4. D. Corresponding parts of congruent triangles are congruent
  5. Triangle ABC is similar to triangle DEF. AB = 6, DE = 9, and BC = 8. What is EF?
    1. A. 72
    2. B. 5 1/3
    3. C. 12
    4. D. 11
  6. A right triangle has legs of 9 and 12. How long is the hypotenuse?
    1. A. 15
    2. B. √63
    3. C. 21
    4. D. 225
  7. A right triangle has a 35° angle and a hypotenuse of 20. To the nearest tenth, how long is the side opposite the 35° angle?
    1. A. 11.5
    2. B. 24.4
    3. C. 14.0
    4. D. 16.4
  8. Each leg of a 45°-45°-90° triangle is 7 units long. How long is the hypotenuse?
    1. A. 7√2
    2. B. 49
    3. C. 14
    4. D. 7√3
  9. sin 40° is equal to the cosine of which angle?
    1. A. 90°
    2. B. 40°
    3. C. 140°
    4. D. 50°
  10. From a point on level ground 40 feet from the base of a flagpole, the angle of elevation to the top is 32°. To the nearest tenth of a foot, how tall is the flagpole?
    1. A. 25.0 feet
    2. B. 64.0 feet
    3. C. 21.2 feet
    4. D. 33.9 feet
  11. A circle has a radius of 6. What is the length of an arc with a central angle of 60°?
    1. A. 12π
    2. B. π
    3. C. 2π
    4. D. 6π
  12. What is the total surface area of a cylinder with radius 3 and height 7?
    1. A. 63π
    2. B. 60π
    3. C. 42π
    4. D. 51π
  13. Which equation describes a circle with center (3, -2) and radius 5?
    1. A. (x + 3)^2 + (y - 2)^2 = 5
    2. B. (x - 3)^2 + (y + 2)^2 = 25
    3. C. (x + 3)^2 + (y - 2)^2 = 25
    4. D. (x - 3)^2 + (y + 2)^2 = 5
  14. What is the area of a regular hexagon with side length 4?
    1. A. 12√3
    2. B. 96
    3. C. 24√3
    4. D. 48√3
  15. A trapezoid has bases of 8 cm and 14 cm and a height of 5 cm. What is its area?
    1. A. 55 square cm
    2. B. 40 square cm
    3. C. 110 square cm
    4. D. 70 square cm

Part 2: Written Response

  1. A student 5 feet tall casts a 3-foot shadow. At the same time, a building casts a 48-foot shadow. (a) Explain why the two triangles formed are similar. (b) Find the height of the building. Show your work.

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