Honors Geometry Semester 1 Exam Review. Hour: CB and CA are opposite rays and CD and CA. Show all your work whenever possible.

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1 Honors Geometry Semester 1 Exam Review Name: Hour: Show all your work whenever possible 1escribe what the notation RS stands for Illustrate with a sketch 8 Find the distance between the points (1, 4) and ( 2, 1) 2 What do PQ and QP have in common? 9 The distance between points and is 8 3 raw four points,,,, and, on a line so that and are opposite rays and and are the same ray Find the midpoint of the segment with endpoints (9, 8) and (3, 5) 4 raw two planes that intersect at JK raw PQ so that it intersects JK at point J re JQ and JK coplanar? Explain your answer 11 Find the circumference of the circle Use = in 12 Find the area ll lengths are in centimeters 5 If RS = 44 and QS = 68, find QR Q R S R, S, and T are collinear S is between R and T RS = 2w + 1, ST = w 1, and RT = 18 Use the Segment ddition Postulate to solve for w Then determine the length of RS 13 wooden fence is to be built around a 50 m-by-62 m lot How many meters of fencing will be needed? If the wood for the fence costs $4775 per meter, what will the wood for the fence cost? 7 Find and in the situation shown = x + 16, = 5x + 10, = In the figure (not drawn to scale), MO bisects LMN mlmo = (15x 21) and mnmo = (x + 63) Solve for x and find m LMN L O N M

2 15 momn = (2x +9) and mlmn = (6x 7) ) and moml = 66 Find momn and mlmn N O 24 Justify the conclusion Given: O and O are a linear pair onclusion: O and O are supplement L M 16 The first three members of a sequence are shown How many dots are in the fourth member of the sequence? n = 1 n = 2 n = 3 25 Write a two-column proof Given: O and O are a linear pair Prove: mo + mo = If the pattern were continued, what would be the ratio of the number of unshaded squares to the number of shaded squares in the next figure in the pattern? 26 Given: 1 and 2 form a linear pair; m2 = 100 Prove: m1 = 80 18If PQ = 3 and PQ + RS = 5, then 3 + RS = 5 is an example of the a Substitution Property of Equality b Multiplication Property of Equality c Transitive Property of Equality d Reflexive Property of Equality 19 Name the property which justifies the following conclusion: Given: b + c d = e and d = a onclusion: b + c a = e 27 Given: 3 4 Prove: Name the property which justifies the following conclusion: Given: 18x = 288 onclusion: x = 16 In 21 and 22, identify the property that makes the statement true 21 If XY = MN, then MN = XY 22 If mp = mr and mr = mt, then mp = mt and 2 form a linear pair If m2 = 67, what is m1?

3 28 1 is complementary to 2; 3 is complementary to 2 What theorem, property, or postulate allows you to state that 1 3? 29 Prove the lternate Exterior ngles onverse Theorem Given: 1 7 Prove: l // n t n 30 Given: 1 and 2 are vertical angles; 1 and 3 form a linear pair Prove: 2 and 3 are supplementary angles Given: E bisects G Prove: G GE 32 In the figure, // n and r is a transversal Which of the following is not necessarily true? a 8 2 c 5 3 b 2 6 d r n 33 dirt path connects the lanes of a divided highway that runs east-west n officer in a police car headed east gets a call that requires crossing over to the westbound lanes using the dirt path Through what angle must the police car turn at the bend in the dirt path? Westbound Lanes 46 Eastbound Lanes 38

4 34 Given that a // b, what is the value of x? (The figure may not be drawn to scale) 29 x Which lines, if any, can be proved parallel given the following diagram? For each conclusion, provide the justification a b a b c d 38 Which best describes the relationship between the line that passes through (7, 1) and (10, 5) and the line that passes through ( 8, 5) and ( 5, 9)? a same line b perpendicular c neither perpendicular nor parallel d parallel 39 Find the slope of a line perpendicular to the line containing the points (3, 7) and (4, 3) ecide whether Line 1 and Line 2 are parallel, perpendicular, or neither Line 1 passes through (4, 6) and (6, 2) Line 2 passes through (7, 8) and (11, 6) 36 Find the slope of the line passing through the given points a (6, 5) and ( 5, 7) 41 Tell whether the lines through the given points are parallel, perpendicular, or neither Explain Line 1: (2, 2), (4, 5) Line 2: (4, 9), (6, 4) b (-2,-3) and (5,3) 42 Find the slope-intercept form of the line passing through the point (9, 8) and parallel to the line y = 8x onsider the line graphed at the right (scaled by 1) In standard form, write the equation of the line 8 43 Identify the x- and y-intercepts of the graph of the equation 6x 4y = 2? Graph the linear equation 8x 2y = 12 by finding x- and y-intercepts 8 a perpendicular to this line through the point (4, 3) b parallel to this line through the point (5, 3) 45 Find the measure of the interior angles to the nearest tenth (rawing is not to scale) (2x + 2) (x + 1) (2x + 1)

5 46 Refer to the figure below Find m Given:, Prove: Find x 48 Solve for x, given that Is equilateral? 7 x 3 53 Given:, Prove: x 1 49 Refer to the figure shown Which of the following statements is true? U T V W TV WV UV XV X a b TUV XWV by S TUV VWX by SS c d TUV WXV by SS TUV WXV by SSS 54 Given: PR and QS bisect each other Prove: PQR RSP P Q T S R 50 State two postulates or theorems that can be used to conclude that O O O 51 Find the length of LM State the postulate or theorem you use M L 350 N 350 P 290

6 55 Given mwxy = mwyx; WX = 3n + 5, WY = 6n 3; Y XY = 9; find WX X W 63 One way to show that two triangles are similar is to show that a two angles of one are congruent to two angles of the other b two sides of one are proportional to two sides of the other c a side of one is congruent to a side of the other d an angle of one is congruent to an angle of the other 64 Shown at the right is an illustration of the Mr Jones has taken a survey of college students and found that 60 out of 64 students are liberal arts majors If a college has 7723 students, what is the best estimate of the number of students who are liberal arts majors? The postulate or theorem that can be used to prove that the two triangles are similar is 57 worker in an assembly line takes 5 hours to produce 26 parts t that rate, how many parts can she produce in 20 hours? 66 In JKL, JK = 10, KL = 13, and L J = 8 In STR, TR = 30, RS = 39, and ST = 24 State whether the triangles are similar, and if so, write a similarity statement 58 Solve the proportion 5 x 1 7 x 67 Find the value of x to one decimal place 59 While visiting a daycare center, you estimate the ratio of toddlers to infants as 3 : 2 If the center has an enrollment of 30 children, about how many of them are infants? 68 For the figure shown, which statement is not true? x w 60 triangle with a perimeter of 63 feet has side lengths in the extended ratio of 6 : 7 : 8 Find the side lengths of the triangle a z y w x b wx = yz c wz = xy d w y y z x z 69 Given: PQ // Find the length of 12 P Q 61 Use the figure to find me The figure is not drawn to scale 19 E The dashed triangle is the image of the solid triangle formed by a dilation centered at the origin What is the scale factor? (x-scale = y-scale = 1) Late in the afternoon, a man who is 6 feet tall casts a 15-foot shadow He is not far from a tower 68 feet tall How long, in feet, is the shadow of the tower?

7 Use the diagram for Exercises 71 and Name the vector and write its component form 75 What is the component form of the vector that describes the translation of a point P(6, -3) to P (-2, 4)? 8, 7 8, 7, 7 8 8, 7 76 a Translate the triangle 4 units up and 2 units left Graph and label image b Find the coordinates of the vertices P,Q and R after the translation c Write the components form of the vector that describes the translation 77 What are coordinates of the image of the point (4, 5) when it is reflected over the line y = 2? (2, 5) (4, 3) (0, 5) (4, -1) 78 The point J(4, 3) is reflected over the line x = 3 It is reflected again over the line x = -1 What are the coordinates of the resulting point? (-2, 3) (2, 3) (-4, 3) (0, 3) 79 The endpoints of are (2, 1) and (3, -1) Graph the line segment and then reflect the segment over the line y = -x dilation with its center at the origin maps (9, -12) to (15, -20) What is the scale factor?

8 k = 3 4 k = 4 5 k = 3 5 k =6 82 The vertices of LMN are L(1, 3), M(3, 2), and N(2, 4) Graph LMN and its image after the glide reflection Translation (x, y) (x + 1, y 6) Reflection: in the y-axis 83 The endpoints of PQ are P(3, -1) and Q(4, -2) What are the coordinates of the endpoints after a rotation of 90 about the origin, followed by a reflection in the line y = x? P (-3, 1), Q P (3, 1), Q (-4, 2) (4, 2) P (-1, 3), Q P (-1, -3), Q (-2, 4) (-2, -4) 84 The vertices of are (1, 6), (6, 4) and (3, 7) Find the coordinates of the vertices after a composition of the transformations listed Translation : (x, y) (x 2, y + 3) Rotation: 180 about the origin Reflection: in the x-axis 85 How many lines of symmetry does a regular hexagon have? How many lines of symmetry does the object at right have? escribe the line symmetry and rotational symmetry of a regular nonagon 88 Identify the line symmetry and rotational symmetry of the figure at the right 6 lines of symmetry, 60 rotational symmetry 3 lines of symmetry, 60 rotational symmetry 6 lines of symmetry, 120 rotational symmetry 3 lines of symmetry, 120 rotational symmetry 89 Identify the coordinates of the image point formed after ( 1, 3) is reflected over the x-axis 90 Identify the coordinates of the point ( 5, 3) after a rotation of 180 clockwise about the origin 91 What is the translation image of (5, 7) after the translation (x, y) (x 2, y + 4)? 92 93

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