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Name:____________________________________Date:_____________Period:________ Semester 1 Geometry Review Chapter 1 and 2: 1. Find the value of each variable: a. . b. 2. πβ π΅π·πΎ = 3π₯ + 4 πππ πβ π½π·π = 5π₯ β 10 ππππ π‘βπ πβ πΎπ·π½. 3. Chapter 3: 4. What type of angle pair are angle 2 and angle 10. 5. If mβ 7 + πβ 6 = 180, which two lines are parallel, how do you know? 6. If π β₯ π, πβ 5 = 2π₯ + 4, πππ πβ 11 = 5π₯ β 8. Find the value of x. 7. The angles in a triangle are in the ratio 2:3:4 find the angle measures. 8. Find the value of x: Chapter 4: 9. Are the two triangles congruent? If so, how do you know? Write a congruence statement if possible: a. b. c. 10. Find the value of x: 11. Given: Μ Μ Μ Μ πΎπΏ β Μ Μ Μ Μ Μ ππ πππ Μ Μ Μ Μ πΎπΏ β₯ Μ Μ Μ Μ Μ ππ Prove: Μ Μ Μ Μ Μ πΎπ β Μ Μ Μ Μ πΏπ 5-1: Midsegments 12. Using the picture to the right, list the parallel segments 13. Using the picture to the right, and RT = 15, DT = 10, and DE = 50 a. FE = b. TF = 14. Find the value of x. 5-2: Perpendicular and Angle Bisectors 15. Find the value of x: 5-3: Bisectors on Triangles and 5-4: Medians and Altitudes 16. Name the point of concurrency for: c. Medians d. Angle bisectors e. Perpendicular bisectors f. Altitudes 17. Find the value of x: 18. Given that Y is the centroid and WY = 4, find TY and TW. 5-5 Indirect Proof 19. Write the first step in an indirect proof proving that at least one angle is acute. 5-6/5-7: Inequalities within triangles: 20. Can 2, 4, and 6 be the sides of a triangle? 21. List the angles in order from smallest to largest in 22. If two sides of a triangle are 5 and 6, find the range for the third side. 23. Using inequalities compare the two side lengths given: 6-1: Polygon angle sum 24. Find each of the following for a heptagon: a. Sum of the interior angles b. Sum of the exterior angles c. One exterior angle (for a regular heptagon) d. One interior angle (for a regular heptagon) 6-2: Parallelograms 25. Find the value of the variable given: e. QT = 3x -5 and TS = 2x + 6 f. πβ πππ = 5π₯ β 1 πππ πβ ππ π = 3π₯ g. PQ = 4x β 5 and RS = 7x β 8 h. πβ πππ = 6π₯ β 3 πππ πβ π ππ = 4π₯ β 7 6-3: Proving Quadrilaterals are Parallelograms 26. Complete the proof: 6-4: Properties of Rectangles, Rhombuses and Squares 27. Find the measure of each numbered angle in the Rhombus: 28. LMNP is a rectangle. Find the value of x and the length of each diagonal. LN = 9x β 14 and MP = 7x + 4. 29. Find the value of x and y. 6-5: Conditions for Rectangles, Rhombuses, and Squares 30. Can you conclude that each parallelogram is a rectangle, rhombus, or square? Explain. i. . b. c. 31. A carpenter is building a bookcase. How can the carpenter use a tape measure to check that the bookshelf is rectangular? Justify your answer. 6-6: Trapezoids and Kites 32. Find the measure of each numbered angle: j. . b. 33. Find the value of x. k. b. . 7-2: Similar Polygons and 7-3: Proving Triangles are Similar 34. Are the polygons similar? If so, write a similarity statement and find the similarity statement. a. b. 35. The polygons are similar. Find the value of x and y. b. b. 7-4: Similarity in Right Triangles 36. Write the similarity statement for the three triangles: 37. What is the geometric mean between 4 and 10? 38. Find the value of each variable: 7-5: Proportions in Triangles 39. Find the value of x: