Geometry Fall Midterm Review 2024 PDF

Geometry Fall Midterm Review 2024 Name ____________________________________________________ My Midterm is on _________________ at __________________ UNIT 1: Basics of Geometry 1. If B is the midpoint of 𝐴𝐶 and AB = 2x – 3 and BC = 5x – 24,...

Geometry Fall Midterm Review 2024 Name ____________________________________________________ My Midterm is on _________________ at __________________ UNIT 1: Basics of Geometry 1. If B is the midpoint of 𝐴𝐶 and AB = 2x – 3 and BC = 5x – 24, find x, AB, and BC. __________ 2. If X is between B & F and XB = 14 and XF = 20, find BF. __________ 3. Find 𝑚∠𝐴𝐵𝐶 if 𝐵𝐷⃗ bisects ∠𝐴𝐵𝐶 and 𝑚∠𝐴𝐵𝐷 = (𝑥 + 11)° and 𝑚∠𝐷𝐵𝐶 = (5𝑥 − 1)°. _______ 4. If 𝑚∠𝐹𝐵𝐶 = 38°, 𝑚∠1 = (3𝑥)°, and 𝑚∠2 = (𝑥 + 2)°, solve for x. ___________ 5. Find the distance between the given endpoints: a. A(-2, -4), B(3, 8) ______ b. E( 2, 1), F(5, 1)_____ 6. Find the midpoint of the segment having the given endpoints: a. A(-2, -4), B(3, 8) ______ b. E( 2, 1), F(5, 1)_____ Refer to Figure 2. Matching, you may use more than one letter to describe the angle(s). ________ 7. ∠1 and ∠2 a. acute angles ________ 8. ∠1 and ∠5 b. right angles C c. obtuse angles B D ________ 9. ∠4 and ∠AOD d. adjacent angles 3 2 A 1 4 E ________ 10. ∠1 and ∠BOE e. linear pair O 5 6 ________ 11. ∠1 and ∠6 f. complementary angles F G ________ 12. ∠AOC and ∠COE g. supplementary angles h. vertical angles Figure 2 i. congruent angles Refer to figure 2 above to solve problems 13-18. 13. If m∠3 = 27°, then m∠4 = _____ 14. m∠1 + m∠BOD = m∠_____. 15. If 𝑂𝐷⃗ bisects ∠COE, then m∠4 = _____. 16. If 𝑂𝐷⃗ ⊥ 𝐵𝐹 , then m∠4 + m∠5 = _____. 17. If 𝑂𝐷⃗ ⊥ 𝐵𝐹 and m∠4 = 65°, then m∠1 = _____, m∠2 = _____, m∠6 = _____, m∠AOF = _____. 18. If ∠𝐹𝑂𝐺 = 34°, find ∠𝐺𝑂𝐵. __________ UNIT 2: Logic & Reasoning Use the following statement for problems # 1 - 4. “If we won the division title, then we are in the playoffs.” 1. Underline the hypothesis and circle the conclusion. 2. Write the converse of the statement. 3. Write the inverse of the statement. 4. Write the contrapositive of the statement For problems 5-10, name the property indicated. Transitive Property Addition Property Substitution Symmetric Property Subtraction Property Combine Like Reflexive Property Multiplication Property Terms/Simplify Distributive Property Division Property 5. If 5𝑥 − 5𝑦 = −3𝑧 and −3𝑧 = 5, then 5𝑥 − 5𝑦 = 5. __________________________________ 6. 3=3 __________________________________ 7. 𝑦 = 𝑥 + 4𝑥 − 1, then 𝑥 + 4𝑥 − 1 = 𝑦. __________________________________ 8. If 𝑈𝑉 ≅ 𝑊𝑋, then 𝑊𝑋 ≅ 𝑈𝑉. __________________________________ 9. 𝑅𝑆 ≅ 𝑅𝑆 __________________________________ 10. If ∠𝐶 ≅ ∠𝐷 and ∠𝐷 ≅ ∠𝐸, then ∠𝐶 ≅ ∠𝐸. __________________________________ 11. Complete the Proof: Given: 3( x  5)  6 x  18 Prove: x = 11 UNIT 3: Parallel Lines & Transversals Refer to figure 3 to solve problems 1-2. 2 1. Given: m∠1 = 3x + 5 and m∠3 = 65, x = _____ 1 3 4 Figure 3 2. Given: m∠2 = 9x +28 and m∠3 = 47 – 2x, x = _____, m∠2 = _____ B C Refer to figure 4 to solve problems 3-4. A O 3. Name an angle complementary to ∠𝐵𝑂𝐶. _________________ D E 4. Name an angle supplementary to ∠𝐴𝑂𝐶. _________________ Figure 4 Solve for x: 5. 3x + 138 6. 4x + 14 3x + 28 2x + 30 7. 3x + 138 8. 3x + 24 5x + 18 2x + 30 9. ∠1 and ∠2 are a linear pair. 𝑚∠1 = 73°. Find the 𝑚∠2. _________________ 10. Classify each pair of angles as one of the following (refer to figure 5): a) alternate interior angles b) same-side interior angles, c) corresponding angles d) alternate exterior angles e) vertical angles f) linear pair g) none of these a b 14 l 4 16 _____a. ∠1 & ∠8 _____b. ∠3 & ∠5 1 15 3 13 2 _____c. ∠3 & ∠10 _____d. ∠10 & ∠12 12 11 m 5 7 9 10 _____e. ∠3 & ∠7 _____f. ∠4 & ∠7 6 8 _____g. ∠7 & ∠8 _____h. ∠2 & ∠13 Figure 5 11. Refer to figure 5 to determine which lines (if any) are parallel. a. Given: ∠1 ≅ ∠5 _____ b. Given: ∠8 ≅ ∠12 _____ c. Given: ∠7 ≅ ∠13 _____ d. Given: ∠6 ≅ ∠11 _____ e. Given: ∠3 and ∠13 are supplementary _____ a b 14 l 12. Given 𝑎 ∥ 𝑏, 𝑙 ∥ 𝑚. (Refer to figure 5) 4 16 1 15 3 13 2 a. If m∠ 12 = 67o , then m∠ 8 = ______ 12 11 m 5 7 b. If m∠ 6 = 108o, then m∠ 4 = ______ 9 10 6 8 c. If m∠ 13 = 123o, then m∠ 12 = ______ d. If m∠ 1 = 71o, then m∠ 5 = ______ Figure 5 e. m∠1 = 2x + 7 and m∠16 = x + 30, x = _____, m∠1 = _____, m∠16 = _____ f. m∠2 = 11x - 16 and m∠7 = 7x + 28, x = _____, m∠2 = _____, m∠7 = _____ 13. Write a Proof: m n Given : 𝑎 ∥ 𝑏 𝑎𝑛𝑑 𝑚 ∥ 𝑛 5 6 1 2 Prove: ∠4 ≅ ∠10 8 7 b 4 3 9 10 13 14 12 11 a 16 15 UNIT 4: Triangle Properties Find the value of x. 2. In ΔABC, find x and m∠A, then classify the 1. x = _______ type of triangle according to sides (scalene, isosceles, equilateral) and angles (right, acute, obtuse, equiangular) 100° 𝑚∠𝐴 = 6𝑥 − 24, 𝑚∠𝐵 = 2𝑥 − 7, 𝑚∠𝐶 = 𝑥 + 4. x° x = ______, 𝑚∠𝐴 = Classifications: ____________________ 3. Using the given information, classify each triangle according to its sides (scalene, isosceles, equilateral) and angles (right, acute, obtuse, equiangular) a. 𝛥𝑀𝑁𝑂, 𝑚∠𝑀 = 27° and 𝑚∠𝑂 = 82°. b. 𝛥𝐴𝑊𝑉, AW = AV and m∠A = 90. c. 𝛥𝐿𝐽𝑅, 𝑚∠𝐿 = 35° and 𝑚∠𝑅 = 104°. d. 𝛥𝑃𝑂𝑁, PO = 5, ON = 5, PN = 5. e. 𝛥𝐿𝐽𝐼, 𝑚∠𝐿 = 45° and 𝑚∠𝐼 = 90°. f. 𝛥𝑆𝑌𝑋, 𝑚∠𝑆 = 60° and 𝑚∠𝑌 = 60°. 4. Identify the longest and shortest side. A P 60° 47° 55° Q R B C a. longest ______ b. longest ______ shortest ______ shortest ______ 5. Identify the smallest and largest angle. A A 24 C 7 3 32 20 B C B 5 a. smallest ______ b. smallest ______ largest _______ largest _______ 6. Fill in the blank with either. a. AC ______CD b. CB ______CD B C D C 19 17 25° 38° 18° D 40° A 19 A 17 B 6. Two sides of a triangle have sides 5 and 9. The length of the third side must be greater than _______ and less than _______. 7. Label the pictures below using these words: Altitude, Midsegment, Median, Perpendicular Bisector, Angle Bisector UNIT 5: Right Triangles 1. Find the length of the leg of this right 2. If the bottom of a 13ft. ladder is 5ft. from triangle. Give an approximation of 3 the wall, how far up the wall does the decimal places. ladder reach? 23 a 17 3. Find the altitude of an isosceles triangle 4. How long is a cable reaching from the top whose base is 10 and whose congruent of a 14 ft. pole to a point on the ground 12 ft. sides are 9. from the pole? 5. Choose the sets that are possible side lengths of a right triangle. a. 1, 1, 2 c. 1, 1, 2 b. 3, 4, 7 d. 3, 4, 5 6. For each set of numbers, determine whether the numbers represent the lengths of the sides of no triangle, an acute triangle, a right triangle, or an obtuse triangle. a) 6, 9, 12 b) 38 , 25 , 13 c) 3.2, 4.2, 5.2 d) 3, 4, 7 7. Find the value of x and y. x 8 y 14 45 14° 30° 30° y x 8. The shorter leg of a 30°, 60°, 90° triangle 9. The leg of an isosceles right triangle is 10 is 8.3 inches long. Find the perimeter and inches long. Find the perimeter and area of area of the triangle. the triangle. 10. An equilateral triangle has side 11. An equilateral triangle has side length of 10. The length of the length of 12. The length of the altitude is ____________. altitude is ___________. UNIT 6: Trigonometry 1. What is x to the nearest hundredth? 2. Write sin A, cos A and tan A. B 13 5 11 x A C 33 12 sin A: _____ cos A: _____ 3. Solve the right triangle. tan A: _____ R 60° Q 34 P For 4-9 solve for x to the nearest tenth. 4. 5. 126 x 53 59° 21° x 6. 7. 65° x x 23° 463 91 8. 9. 18 𝑥° 87 136 59 𝑥°