2 Geometry Midterm Exam Review Name: __________________________________________ Period: _________ Chapter 1: Essentials of Geometry 1. Give another name for line 𝑙 . 2. Name the intersection of line 𝑚 and plane G. 3. Name the intersection of lines 𝑙 and line 𝑚. 4. Name three points that are coplanar. 5. Find the indicated length. Find HJ : Find XZ: In exercises 6-­‐7, find the midpoint between the two endpoints. 6. T(3, 9) and W(15, 5) 7. C(1, 4) and D(3, 2) In exercises 8-­‐9, find the distance between the two points. 8. T(3, 4) and W(2, 7) 9. C(5, 10) and D(6, -­‐1) 2 Geometry Midterm Exam Review In exercises 10-­‐12, find the measure and classify the angle in the figure. 10. ∠𝐴𝑀𝑉 11. ∠𝐷𝑀𝑉 12. ∠𝑉𝑀𝐸 In Exercises 13-­‐14, use the diagram at the right. 13. Find x. 14. Find the m ⦟DEG and m⦟ GEF. 
15. The measure of ∠LOM is 21°. OM bisects ∠LON . a.) What is the measure of ∠LON ? b.) What is the measure of ∠MON ? 16. If ∠1 𝑎𝑛𝑑 ∠2 are complements, and ∠1 = 12°, find the measure of ∠2 17. If ∠1 𝑎𝑛𝑑 ∠2 are supplements, and ∠1 = 12°, find the measure of ∠2 18. A complementary pair of angles have the measurements (x -­‐10) and (2x + 40) Find the measures of each of the angles. 2 Geometry Midterm Exam Review 19. What is the name of the polygon that has seven sides? _______________________ 20. Determine whether the polygons below are equiangular, equilateral, regular, or none. 21. Two side lengths of a regular polygon are represented by the expressions 10𝑥 − 42 𝑎𝑛𝑑 6𝑥 + 10. Find x. 22. Decide whether the figure is a polygon. If it is, state whether it is convex or concave. 23. Find the area and perimeter of the triangle (use formula sheet). 2 Geometry Midterm Exam Review 24. Find the circumference and area of a circle with a radius of 10 cm. Use 3.14 for pi. 25. A square has a perimeter of 100 square units. What is its area? 26. Chapter 2: Reasoning and Proof Hypothesis-­‐ __________________________________________ Conclusion-­‐ __________________________________________ 27. Write the converse, inverse and the contrapositive for the given conjecture. a.) If an animal is a frog, then it is an amphibian. -­‐Converse: -­‐Inverse: -­‐Contrapositive: 28. Find a counterexample for the converse of statement 26. 2 Geometry Midterm Exam Review 29. Rewrite the statement as a biconditional statement. “An angle with a measure between 90° and 180° is called obtuse. 30. Match the property with the property that it illustrates. Chapter 3: Parallel and Perpendicular Lines 31. What line is parallel to CD and contains point E? 32. What line is skew to CD and contains point E? 33. What line is not parallel to plane CBG? 34. Which plane is parallel to plane CBG? 35. Classify the pairs of angles as corresponding, alternate interior, alternate exterior, or consecutive interior. a.) ∠1and∠8 b.) ∠4and∠5 c.) ∠2and∠6 d.) ∠3and∠6 36. If the measure of ∠2 = 50°, what is the measure of ∠5? 2 Geometry Midterm Exam Review 37. Find the value of x (or y) a.)
b.) c.) 38. A line on the coordinate plane passes through (2, 1) (0, 6). Find the slope of the line. 40. Which pairs of lines are parallel? Line a (3, -­‐4) and (-­‐1, 4) Line b (8, 12) and (7, -­‐5) Line c (2, 7) and (5, 1) 41. Write an equation of the line that passes through the given point P (-­‐2, 4) and has the slope m = 3. 42.) Write an equation of the line that passes through point P (-­‐1, 1) and is parallel to the equation y = 2x – 3. 2 Geometry Midterm Exam Review 43.) Write an equation of the line that passes through point P and is perpendicular with the equation. a.) (1, 3), y = 2x – 1 b.) P(3, 4), y = -­‐1/6x -­‐ 10 44) Identify the equation of the graph shown. Chapter 4: Congruent Triangles By sides: scalene isosceles By angles: acute obtuse 45. Classify the triangle by its side and its angles. a.) b.)
equilateral right c.)
equiangular 2 Geometry Midterm Exam Review 46.) Find the value of x. Use the interior angle theorem 47) Find the value of x. Use the exterior angle theorem. 48) Find the value of x. Use the properties of isosceles triangles. 2 Geometry Midterm Exam Review 49) The valid congruency postulates are: ____________, _______________, ______________, ___________, _______________ 50. Determine whether the triangles can be proven congruent by the given postulate. a.)
b.)
c.) 51. Determine whether the triangles are congruent. If so, identify the congruency postulate. If not, say not enough information. S
R
T
U
Chapter 5: Relationships with Triangles 52. Segment MP is a midsegment of the triangle. What is the measurement of MP? 53. BD is a perpendicular bisector of the triangle. Find x. 2 Geometry Midterm Exam Review 54. 55. 56. In this triangle, P is the centroid and SL=18. Find SP and PL. 57. 58. In this triangle, which side is the longest? 2 Geometry Midterm Exam Review 59.) Is it possible to construct a triangle with the given side lengths? a. 4, 11, 15 b. 3, 11, 15 c. 5, 11, 15 60.) A triangle has one side length of 12 and another length of 8. Describe possible side lengths of the third side. Chapter 6: Similarity 61. The angles of a triangle have measures in an extended ratio of 1:3:5. Find the measure of the largest angle. 62. a.) Find the scale factor between the two triangles. b.) Set up a proportion and find x. 63. In the picture below, JKLM is similar to EFGH. Find the value of x, y, and z.