# 7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI.

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1 1. Name three points in the diagram that are not collinear. 2. If RS = 44 and QS = 68, find QR. 3. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition Postulate to solve for w. Then determine the length of 7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI. 4. If AB = 19 and AC = 32, find the length of Fill in the correct word(s) to make the statement true. 5. Mathematical statements that are assumed to be true are called. BC = 7x 13, AB = 4x + 26, B is the midpoint of. 8. The measure of angle A is 98. Classify angle A as an acute, right, or obtuse angle. 9. The nonshared sides of two adjacent angles form a pair of opposite rays. The angles are. a. acute b. complementary c. a linear pair d. vertical angles 6. Find AB and BC in the situation shown above.

2 Complete the conditional statement to make a true statement If and are complementary and, then Name a pair of vertical angles in the figure above. 11. If and are supplementary and, then Solve for x: Name an angle supplementary to above. in the figure ( 4x + 90 ) (2x + 72 ) 13. form a linear pair.. Find. 19. Complete the table. 16. Complete the statement. A regular polygon is both and equiangular. 17. The expressions represent two side lengths (in meters) of a regular octagon. Find the length of a side of the octagon. 18. The expressions represent two angle measures of a regular pentagon. Find the measure of an angle of the pentagon. n nth number 1 3 5??? 20. Rewrite the statement in if-then form. Every triangle has three sides. 21. "If an obtuse angle is bisected, then two acute angles are obtained." Write the converse of this conditional statement. Is the converse true? 22. Write the converse of the true statement and decide whether the converse is true or false. If the converse is true, combine it with the original statement to form a true biconditional statement. If the converse is false, state a counterexample: If an angle has a measure of 90, then it is a right angle. 23. Rewrite the postulate in if-then form. "A line contains at least two points." 24. Sketch a diagram showing the following: Line m is perpendicular to segment AB at P, the midpoint of segment AB.

3 28.Solve for x. 30. form a linear pair. If, what is 31. are supplementary angles. are vertical angles.. Find. 33. Two lines that are not coplanar and do not intersect are called. a. Parallel c. perpendicular b. oblique d. skew lines 34. In the figure, and are. 35. In the figure, are. 36. In the figure, are. 37. In the figure below, if l and k are parallel lines, what is the value of x and y?

4 39.Find the value of x: 40. Use the figure below to solve for x. 41. What is the value of z? (The figure may not be drawn to scale.) 42. Given:. Complete the statements. a. b. 43. Identify the congruent triangles. How do you know they are congruent?

5 44.What must be true in order for SAS Congruence Postulate? by the Line l is the perpendicular bisector of. 48. Find the value of x. a. b. c. d. 50. What is the measure of each base angle of an isosceles triangle if its vertex angle measures 40 degrees and its 2 congruent sides measure 25 units? 45. Identify the congruent triangles. How do you know they are congruent? 46. Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent? 51. Find the values of x and y. 47. Which postulate or theorem can be used to determine the length of?

6 52.Solve for x given = and =. Assume B is the midpoint of and D is the midpoint of 55. In the diagram, X is the incenter of. Find XU. C B D Refer to the figure below. A E 53.Refer to the figure below. Given:, ABE EBC 56. A median of is. Given: Which line is a perpendicular bisector in? 54. Find the value of z. Is there enough information to show that D lies on the vertical line that passes through B? 58. Which of these lengths could be the sides of a triangle? a. 15 cm, 4 cm, 20 cm b. 3 cm, 15 cm, 20 cm c. 11 cm, 5 cm, 16 cm d. 5 cm, 12 cm, 16 cm 59. If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. Use this fact to help you list the sides of triangle TUV in order from greatest to least. (The figure may not be drawn to scale.)

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Geometry Unit 2 Reasoning and Proof 2-1 Conditional Statements Conditional Statement a statement which has a hypothesis and conclusion, often called an if-then statement. Conditional statements are contain

Chapter 3 Cumulative Review Answers 1a. The triangle inequality is violated. 1b. The sum of the angles is not 180º. 1c. Two angles are equal, but the sides opposite those angles are not equal. 1d. The

### Chapter 2. Worked-Out Solutions Quiz (p. 90)

2.1 2.3 Quiz (p. 90) 1. If-then form: If an angle measures 167, then the angle is an obtuse angle. (True) Converse: If an angle is obtuse, then the angle measures 167. (False) Inverse: If an angle does

### Chapter 2 Test Review

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### Geometry Semester 1 Exam Released

1. Use the diagram. 3. In the diagram, mlmn 54. L 5 1 4 3 2 Which best describes the pair of angles 1 and 4? (A) complementary (B) linear pair (C) supplementary (D) vertical 2. Use the diagram. E F A B

### Higher Geometry Problems

Higher Geometry Problems (1) Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement

### 0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.

0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation