Geometry (Grades 9–10) Midterm — Units 3–4

Part 1: Multiple Choice

1. What is the measure of each exterior angle of a regular octagon?
   1. A. 135°
   2. B. 40°
   3. C. 60°
   4. D. 45°
2. Which line is parallel to y = 3x - 2?
   1. A. y = -3x - 2
   2. B. y = -(1/3)x + 4
   3. C. y = 3x + 7
   4. D. y = (1/3)x - 2
3. The vertex angle of an isosceles triangle measures 40°. What is the measure of each base angle?
   1. A. 40°
   2. B. 70°
   3. C. 140°
   4. D. 50°
4. Two parallel lines are cut by a transversal. A pair of alternate interior angles measure (3x + 15)° and (5x - 25)°. What is x?
   1. A. 65
   2. B. 20
   3. C. 23.75
   4. D. 5
5. What is the sum of the interior angle measures of a hexagon?
   1. A. 360°
   2. B. 1,080°
   3. C. 540°
   4. D. 720°
6. Two parallel lines are cut by a transversal. One same-side interior angle measures 110°. What is the measure of the other same-side interior angle?
   1. A. 20°
   2. B. 250°
   3. C. 70°
   4. D. 110°
7. Two angles of a triangle measure 50° and 65°. What is the measure of the third angle?
   1. A. 75°
   2. B. 245°
   3. C. 65°
   4. D. 115°
8. Two parallel lines are cut by a transversal. One angle measures 65°. What is the measure of its corresponding angle?
   1. A. 115°
   2. B. 130°
   3. C. 25°
   4. D. 65°
9. Two sides of a triangle measure 7 and 12. Which inequality describes all possible lengths x of the third side?
   1. A. 5 < x < 19
   2. B. 7 < x < 12
   3. C. 0 < x < 19
   4. D. 5 ≤ x ≤ 19
10. The two remote interior angles of a triangle measure 40° and 75°. What is the measure of the exterior angle at the third vertex?
    1. A. 115°
    2. B. 65°
    3. C. 245°
    4. D. 35°
11. 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°
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. 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

Part 2: Written Response

21. 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.