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1st Semester Practice Final Name: __________ ____ Date: Period: _________ 1st Semester Final Score Grade Multiple Choice & Fill in the Blank / / 1.1 Angle Relationships Pr 1, 2, 3, 5, 9 / 16pts / 1.2 Triangle Angle Relationships Pr, 4, 10, 11, 12, 13, 14 / 11pts / 2.1 Pythagorean Theorem Pr 15, 16 / 4 pts / 2.2 Right Triangle Trig Pr 17, 18, 19, 20, 21 / 10 pts / 2.3 Special Right Triangles Pr 22, 23, 24 / 11 pts / 3.1 Standard Transformations Pr 6, 7, 8 / 6 pts / 4.1 Prove Triangle Similarity Pr 29, 30 / 8pts / 4.2 Triangle Congruency Pr 25, 26, 27, 28 / 17pts / 5.1 Angles in a Regular Polygon Pr 31, 32 Final Score / 18 pts / / 101 pts / 1. Given parallel lines cut by a transversal, alternate-side exterior angles are . . . (Circle any that apply 1 point) Congruent Supplementary Complementary Corresponding Adjacent Hypotenuse 2. Two angles are complementary if they… (Circle any that apply 1 point) Are equal Are congruent Are inside parallel lines Add to 180 Add to 90 3. For each diagram find the value of x. (3 points each) Show your work and name the angle relationship(s) you used to solve the problem. a) b) 15x –x + 20 5x + 10 4x – 40 Show Work and Name Relationship(s) Show Work and Name Relationship(s) 1st Semester Practice Final Name: __________ ____ Date: Period: _________ 4. For the diagram find the value of x. Show your work. (2 points) 45° 120° x° 5. Find all the values of the variables shown below. f s j x t r m 150 60 (7 points) f= j= x= s= r= t= m= 6. What are the new coordinates after you translate PQR 2 units down and 5 units to the left. A) P'(3, 4) Q'(4, 1) R'(7, 1) B) P'(-7, 0) Q'(-6, -3) R'(-3, -3) P C) P'(0, 7) Q'(1, 4) R'(4, 4) Q R D) None of these. 1st Semester Practice Final Name: __________ ____ Date: Period: _________ 7. What are the coordinates of B' after the ∆ABC is dilated about the origin with a zoom factor of 2. A) B'(10, 4) A(1,2) B(5,2) C(3,3) B) B'(15, 2) C) B'(5, 6) D) None of these 8. The point A(6, -4) is rotated 90 counter-clockwise about the origin. The coordinate of A is: A) B) C) D) (-4, 6) (-4, -6) (-6, 4) (4, 6) 9. Given parallel lines cut by a transversal, alternate interior angles are ? A) Perpendicular B) Complementary C) Congruent D) Supplementary 10. In the figure below, find the measures of 1, 2, and 3. (3 points) 2 63º 3 1 1st Semester Practice Final Name: __________ ____ Date: Period: _________ 11. Choose a value for x such that will make this a true triangle. (1 Point) x 8 21 A) x = 13 B) x = 29 C) x = 14 D) x = 32 12. Solve for the measure of x in the diagram to the right. (1 Point) 19 A) 128° B) 52° 14 C) 19° x D) 33° 13. Given isosceles triangle ∆ABC with AB = AC. If A = x + 17 and B = 2x + 4 then C = ? (2 Points) A x + 17 A) 7o B) 16o C C) 30o D) 66o 2x + 4 B E) None of These 14. Find the value of x in the triangle to the right. (2 Points) A) 61 in B) 69.31 in C) 119.101 in D) 97.86 in x 109 .12 40 48" 1st Semester Practice Final Name: __________ ____ Date: Period: _________ 15. Use the Pythagorean Theorem to show whether or not the given lengths of the sides are correct. Is it a right triangle? Circle the correct answer. (2 Points) Show your work. 22 Yes or No 25 5 16. Find the value of x in the triangle to the right. (2 Points) A) 12.1 units 15.199 B) 9.8 units 5 C) 6 units x D) 16 units 6 17. Solve for θ in the following triangle. (2 Points) A) 60° B) 0.37° 12 C) 68.68° ° D) 30° Using trigonometric ratios solve for the missing measurement in the triangles below. (2 Points each) 33° 18. A) 52.9 130 k B) 200.182 C) 118.8 D) 84.42 19. A) 8.99 14 B) 21.78 y 40 C) 15.66 D) 18.66 1st Semester Practice Final Name: __________ ____ 5 20. 8 Date: Period: _________ A) 32° B) 39° θ C) 51° D) 58° 21. Brett is 45 feet from the base of a building. He measures the angle of elevation to the top of the building and finds it is 40°. How tall is the building? (2 Points) A) 412.35 feet B) 37.76 feet C) 53.629 feet D) None of these 22. Fill in the blank with the missing length(s) in each of these triangles. You must express your answers in simple radical form. (4 points) _______ _______ 30 24 60 _______ 45 _______ 23. a. Draw the 45/45/90 triangle ∆𝑃𝑄𝑅 below. Label the angles and side lengths. b. Given that the leg of ∆𝑃𝑄𝑅 is 6in, find the lengths of the remaining sides. 1st Semester Practice Final Name: __________ ____ Date: Period: _________ 24. If the sides of a triangle are 12, 6√2, & 6√2; a. Draw and label a picture of this triangle. (1 point) b. Is this a 30/60/90 or a 45/45/90 triangle? Justify (prove) your response. (2 point) 25. Complete the following proof. (5 points) Statements Reasons 1. QD AU D A 1. 2. Q U 2. Given 3. DU UD 3. 4. ∆QDU ∆AUD 4. 26. For each pair of triangles, decide whether or not they are congruent. If they are congruent, write the congruent statement (ABC ≅ . . .) and the congruence property (SSS, etc.) that proves it. If not, say "not ≅’. NOTE: These are not to scale! (4 points) a. PQR ≅ _________ by . HJK ≅ __________by . H Q V R b. P S M U J K L 1st Semester Practice Final Name: __________ ____ Date: Period: _________ 27. . Prove the following by completing the two column proof below. (6 points) Given: TR RE TRK ERK Prove: T E R Statements Justifications K 1. TR RE 1. 2. 2. Given 3. 3. 4. ∆TRK ∆ERK 4. 5. T E 5. T 28. Complete the following proof. (5 points) D Given: E is the midpoint of AC DE EB A A E B Prove: ∆AED ∆CEB E C Statement Reason 1. 1. Given 2. E is the midpoint of AC 2. 3. 3. Definition of midpoint 4. 4. Vertical angles are equal 5. ∆AED ∆CEB 5. 1st Semester Practice Final Name: __________ ____ Date: Period: _________ 29. Given ABC~WYZ, which of the following could be used to solve for x? (7 point) B x Z A 8 C 40 15 W 20 Y Proportions/Equation Correct Not Correct 𝑥 40 = 20 8 20𝑥 = 40 𝑥 8 = 40 20 𝑥 40 = 8 20 8𝑥 = 128 𝑥 15 = 8 20 8 𝑥 = 20 40 30. Given the triangles to the right, what conjecture can be used to show DEF~TRV? (1 point) T A) SSA~ F 14 B) SAS~ C) ASA~ D) Not ~ 78 D 78 E 6 R 21 9 V 1st Semester Practice Final Name: __________ ____ Date: Period: _________ 31.Fill in the table below with the correct missing information for each regular polygon. (15 points) Number of Sides Single Interior Angle Single Exterior Angle Sum of Interior Angles 10 2700° 72° 20° N 32. Use what you have learned about the angles of a polygon to write an equation and solve for the unknown variable. Show all work. (3 points) 110 (x + 20) x