Geometry Semester 1 Final Review 1. While working on a team quiz, Anna, Bella, and Cortez came across the following problem: B Solve for x and then find the measure of each angle. 2x + 1 Bella quickly solved the problem and told her team “Hey! I got it! mA 93 , mB 63 , and mC 36 . Done!” A x+5 3x C Anna and Cortez are suspicious. Does Bella have the correct answer or are Anna and Cortez correct to be suspicious? Explain completely. 2. Write an equation in slope-intercept form for the line with the given condition that contains the point (6, –2). a. parallel to the line 2 x y 5 ____________________ b. perpendicular to the line y 3x 4 __________________ 3. Determine whether or not each pair of triangles is similar. If they are similar, explain why. If not, state why you know they are not similar or why there is not enough information. Is ∆𝑅𝐴𝑃~∆𝑁𝑂𝐾? Why? a. R 6 Y A N 9 6 P Is ∆𝑅𝐴𝑀~∆𝑌𝐴𝐾? Why? b. 9 A R O M 15 K K 4. Write the converse of each conditional statement. a. If the moon is full, then the vampires are prowling. b. If you do not understand geometry, then you do not know how to reason deductively c. If you live in a mansion, then you have a big heating bill d. You cannot skateboard if you do not have a sense of balance 5. Write each as a conditional statement. a. All Polo shirts have a horse logo. b. A triangle is formed by three segments. c. Linear pairs are supplementary, adjacent angles. d. When you are eighteen you can vote. 6. Find the midpoint of the line segment with the given endpoints. a. (-4, 4), (5, -1) b. (2, 4), (1, -3) 7. Find the other endpoint of the line segment with the given endpoint and midpoint. a. Endpoint: (-9, 7), midpoint: (10, -3) b. Endpoint: (-6, 4), midpoint: (4, 8) 8. Determine whether the following triangles are congruent. If they are give the triangle congruence statement and the congruence shortcut. If they can’t be proven, state “not possible.” a. b. c. e. d. f. 9. For each situation decide if you would use the incenter or circumcenter. a. The first-aid center of Mt. Thermopolis State Park needs to be at a point that is equidistant from three bike paths that intersect to form a triangle. Locate this point so that in an emergency, medical personnel will be able to get to any one of the paths by the shortest route possible. b. Rosita wants to install a circular sink in her new triangular countertop. She wants to choose the largest sink that will fit. c. Julian Chive wishes to center a butcher-block table at a location equidistant from the refrigerator, stove, and sink. 10. Fill in the missing statements or reasons. a. 11. a. Solve for x. b. b. Solve for x. 12. 13. Are the triangles congruent? If so, write a congruence statement. 14. Write a similarity statement showing the two triangles are similar. 15. Graph RS with endpoints R(– 8, 5) and S( – 6, 8). Graph its image after the composition. 16. Graph ∆𝐴𝐵𝐶 with vertices A(3, 2), B(6, 3) and C(7, 1) and its image after the glide reflection. 17. Graph RS with endpoints R(1, -3) and S(2, 0 – 6) and its image after the composition. 18. Graph ∆𝐴𝐵𝐶 with vertices A(3, 1), B(3, 4), and C(1, 1) and its image after a 180° rotation about the origin. 19. Find the scale factor of the dilation. Then tell whether it is a reduction or an enlargement. 20. A photographer enlarges a 4 inch x 5 inch photo to an 8 in x 10 in photo. What is the scale factor of the dilation? 21. Find each measure. c. 22. a. d. b.
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