Find the coordinates of the midpoint of the segment with the given endpoints. Use the midpoint formula.

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Ethelbert Manning
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1 Concepts Geometry 1 st Semester Review Packet Use the figure to the left for the following questions. 1) Give two other names for AB. 2) Name three points that are collinear. 3) Name a point not coplanar with A, C, and T. Use the figure to the right for the following questions. 4) What is another name for XW? 5) Name all rays with endpoint X. Find the indicated length. 6) YZ 7) LN Find the distance between the points using the distance formula. Round to the nearest tenth, if necessary. 8) A(2, 3) and B(4, 9) 9) F( 4, 6) and G(1, 8) Find the coordinates of the midpoint of the segment with the given endpoints. Use the midpoint formula. 10) A ( 1, 4) and B (3, 6)

11) C (2, 3) and D ( 4, 1) 1 and 2 are complementary angles. Given the measure of 1, find m 2. 12) m 1 = 87º 13) m 1 = 15º 1 and 2 are supplementary angles. Given the measure of 1, find m 2. 14) m 1 = 8º 15) m 1 = 87º Use the figure at the right to answer the following questions.

2 11) C (2, 3) and D ( 4, 1) 1 and 2 are complementary angles. Given the measure of 1, find m 2. 12) m 1 = 87º 13) m 1 = 15º 1 and 2 are supplementary angles. Given the measure of 1, find m 2. 14) m 1 = 8º 15) m 1 = 87º Use the figure at the right to answer the following questions. Tell whether the angles are vertical angles, a linear pair, or neither. 16) 1 and 2 17) 2 and 5 18) 1 and 4 19) Find m ABC and m CBD if m ABD = 120.

25) A has a definite starting point and extends without end in one direction. 26) are two rays that are part of the same line and have only their endpoints in common.

3 20) VZ bisects UVW, and m UVZ 21 o. Find m UVW. Then classify UVW by its angle measure. 21) If m 2 = 6x - 1 and the m 4 = 4x + 17, then find the m 3. 22) Draw an example of a concave pentagon. 23) Draw an example of a linear pair of angles. Fill-in the blank: 24) A has a definite beginning and end. 25) A has a definite starting point and extends without end in one direction. 26) are two rays that are part of the same line and have only their endpoints in common. 27) You can use a to measure angles and sketch angles of given measure. 28) Angles with the same measure are. 29) Two angles are if and only if (iff) the sum of their degree measure is ) A regular polygon is both and.

4 31) Describe the pattern in the numbers. Write the next three numbers. -6, -1, 4, 9, 32) Describe the pattern in the numbers. Write the next three numbers. 100, -50, 25, -12.5, 33) Draw the fourth figure in the pattern. Find a counterexample to disprove the conjecture. 34) All intersecting lines form right angles. 35) All quadrilaterals are equilateral. 36) Write the if-then form, the converse, the inverse, and the contrapositive for the given statement. Decide whether each statement is true or false. A soccer player is an athlete. If-then: Converse: Inverse: Contrapositive: 37) Rewrite the definition as a biconditional statement. Coplanar points are points that lie in the same plane.

38) Determine whether the statement is a good definition. Explain your answer. If an angle is a right angle, then its measure is greater than that of an acute angle.

5 38) Determine whether the statement is a good definition. Explain your answer. If an angle is a right angle, then its measure is greater than that of an acute angle. 39) If you decide to go to the football game, then you will miss band practice. Tonight, you are going to the football game. Using the Law of Detachment, what statement can you make? 40) If you get an A or better on your math test, then you can go to the movies. If you go to the movies, then you can watch your favorite actor. Using the Law of Syllogism, what statement can you make? Select the word(s) that make(s) the conclusion true. 41) The Empire State Building is in New York City. Sam vacationed in New York City. So, Sam (must have, may have, or never) visited the Empire State Building. 42) Some tourist sites in New York City are accessible when accompanied by a tour guide. So, Sam (is, may be, or is not) visiting tourist sites in New York City with a tour guide. Use the diagram to write examples of the stated postulate. 43) A line contains at least two points 44) A plane contains at least three noncollinear points. 45) If two planes intersect, then their intersection is a line. 46) Sketch a diagram that represents the given information: straight angle CDE is bisected by DK.

6 47) How can you show that the statement, If you play a sport, then you wear a helmet. Is false? Explain. 48) Use deductive reasoning to make a statement about the picture. 49) If m o,find m 2, m 3,and m 4. 50) Find the value of x. 51) 52) 53) Solve the equation. Write a reason for each step. 5(x 1) = 4x ) Complete the statement. a. 4 and are corresponding angles. b. 3 and are consecutive interior angles. c. 5 and are alternate interior angles. d. 7 and are alternate exterior angles.

7 55) Find the value of x. Explain your reasoning. 56) Find the value of x. Explain your reasoning. 57) Find the value of x. Explain your reasoning. Find the value of x that makes m n. 58) 59) 60) 61) A line that intersects two other lines is a. 62) Draw a pair of parallel lines with a transversal. Identify all pairs of alternate exterior angles.

8 63) Write the slope formula. 64) Find the slope of the line that passes through the points (3, 5) and (5, 6). Tell whether lines through the given points are parallel, perpendicular, or neither. Justify your answer by using the slope formula. 65) Line 1: (1, 0), (7, 4) Line 2: (7, 0), (3, 6) 66) Line 1: (-3, 1), (-7, -2) Line 2: (2, -1), (8, 4) 67) Graph the line through the given point with the given slope. P(3, -2), slope: -3 68) Write an equation of the line that passes through the point (2, -3) that is parallel to the line with the equation y = 6x ) Write an equation of the line that passes through the point (3, -4) that is 1 perpendicular to the line with the equation y x ) Using intercepts method, find the x and y intercept of 3x + 4y = ) Draw a line with an undefined slope on the coordinate plane. 72) Rewrite the equation y + x = 4 in slope intercept form. 73) Write the equation -2x + 3y = 18 in slope intercept form.

9 74) Write two things that you know about parallel lines. 75) Write two things that you know about perpendicular lines. 76) Can a triangle have degree measure of 100 o, 95 o, and 30 o? Explain why or why not. 77) List three types of transformations that are rigid motions. 78) How can you use side lengths to prove triangles congruent? 79) A triangle with three congruent angles is called. 80) Draw right isosceles triangle. 81) Draw an acute scalene triangle. Find the value of x. Then classify the triangle by its angles. 82) 83) 84)

10 85) 86) Find the measure of angle o 1 87) Find m JKM. 88) Write all the congruence statements for the figures. 89) Identify the transformation you could use to move the solid figure onto the dashed figure. 90) Find the values of x and y. ABCD EFGH

91) Explain why the bench with the diagonal support is stable, while the one without support can collapse. Complete the congruence statement for the figures.

11 91) Explain why the bench with the diagonal support is stable, while the one without support can collapse. Complete the congruence statement for the figures. 92) QRS 93) ABCD 94) Explain the difference between proving triangles congruent using the ASA and AAS Congruence Postulates. 95) Explain what CPCTC is an abbreviation for and why is it useful? 96) Are isosceles triangles always acute triangles? Explain your reasoning. 97) The angle between two sides of a triangle is called the angle. 98) When triangles are congruent, you have sets of corresponding congruent parts.

99) Congruent triangles are the same shape and the same. 100) If two triangles are congruent, the corresponding angles are. 101) All angles are congruent.

12 99) Congruent triangles are the same shape and the same. 100) If two triangles are congruent, the corresponding angles are. 101) All angles are congruent. 102) Triangles can be proven congruent using a two-column. Use the given information and explain how you could get two triangles that are congruent, if possible. If you can get two triangles congruent, state your reasoning completely. 103) Q U D A 104) B A D C 105) A T P R S 106) 107)

State the third congruence that must be given to prove that ABC DEF using the indicated postulate. 108) Given: AB DE, CB FE, B E Use the SSS Congruence Postulate.

13 State the third congruence that must be given to prove that ABC DEF using the indicated postulate. 108) Given: AB DE, CB FE, B E Use the SSS Congruence Postulate. 109) Given: A D, CA FD, A C D F Use the SAS Congruence Postulate. 110) Given: BC EF, B E, Use the ASA Congruence Postulate. Find the values of x and y. 111) 5 U 5 M y o 5 3x o D 112) (x+7) o y o 55 o 113) Find the values of angles 1, 2, 3, and ) CAT, by C R A P T THEREFORE:, by CPCTC, by CPCTC, by CPCTC

1) Draw line m that contains the points A and B. Name two other ways to name this line.

1) Draw line m that contains the points A and B. Name two other ways to name this line. 2) Find the next 3 terms in the sequence and describe the pattern in words. 1, 5, 9, 13,,, 3) Find the next 3 terms