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

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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 B
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. Triangle 1 has angles of 40° and 60°. Triangle 2 has angles of 60° and 80°. Which statement is true?
    1. A. They are not similar, since only one listed angle matches
    2. B. They are similar by SSS
    3. C. They are similar by AA, since both have angles of 40°, 60°, and 80°
    4. D. They must be congruent by AAS
  2. Triangle ABC is congruent to triangle DEF. Which statement must be true?
    1. A. Side AB ≅ side EF
    2. B. ∠A ≅ ∠F
    3. C. ∠B ≅ ∠E
    4. D. Side BC ≅ side DF
  3. Which of these is NOT a valid way to prove two triangles congruent?
    1. A. SAS
    2. B. SSS
    3. C. ASA
    4. D. SSA
  4. In a triangle, a segment joins the midpoints of two sides. The third side is 18 cm long. How long is the segment?
    1. A. 36 cm
    2. B. 18 cm
    3. C. 6 cm
    4. D. 9 cm
  5. A 6-foot person casts a 4-foot shadow. At the same time, a tree casts a 22-foot shadow. How tall is the tree?
    1. A. 132 feet
    2. B. 24 feet
    3. C. 33 feet
    4. D. 14.7 feet
  6. A right triangle has legs of 7 and 24 and a hypotenuse of 25. Angle θ is opposite the side of length 7. What is cos θ?
    1. A. 7/25
    2. B. 25/24
    3. C. 7/24
    4. D. 24/25
  7. In a 30°-60°-90° triangle, the shorter leg is 5. How long is the longer leg?
    1. A. 10
    2. B. 5√2
    3. C. 15
    4. D. 5√3
  8. A right triangle has legs of 5 and 12. To the nearest tenth of a degree, what is the measure of the angle opposite the side of length 5?
    1. A. 24.6°
    2. B. 65.4°
    3. C. 67.4°
    4. D. 22.6°
  9. A triangle has sides of length 8, 15, and 18. How is it classified by its angles?
    1. A. Acute
    2. B. Obtuse
    3. C. It cannot be a triangle
    4. D. Right
  10. Right triangle ABC has its right angle at C. The side opposite angle A is 8, the side adjacent to angle A is 15, and the hypotenuse is 17. What is sin A?
    1. A. 17/8
    2. B. 8/17
    3. C. 8/15
    4. D. 15/17
  11. An inscribed angle in a circle intercepts an arc of 110°. What is the measure of the inscribed angle?
    1. A. 220°
    2. B. 110°
    3. C. 70°
    4. D. 55°
  12. A line is tangent to a circle. What is the measure of the angle between the tangent and the radius drawn to the point of tangency?
    1. A. 180°
    2. B. 60°
    3. C. 90°
    4. D. 45°
  13. What is the surface area of a sphere with radius 5?
    1. A. 500π/3
    2. B. 25π
    3. C. 50π
    4. D. 100π
  14. A pyramid has a square base with sides of 6 m and a height of 10 m. What is its volume?
    1. A. 360 cubic meters
    2. B. 240 cubic meters
    3. C. 120 cubic meters
    4. D. 60 cubic meters
  15. A circle has a radius of 10. What is the area of a sector with a central angle of 90°?
    1. A. 100π
    2. B. 25π
    3. C. 5π
    4. D. 50π

Part 2: Written Response

  1. A wheelchair ramp rises 2.5 feet and makes a 4.8° angle with the level ground. Find the length of the ramp surface and the horizontal distance it covers, each to the nearest tenth of a foot. Show your work.

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