Chapter Test. and QR. midpoint, S, of RT. Then use the Distance Formula to verify that RS = ST. CHAPTER 1

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1 Use the diagra to nae the figures.. hree collinear points. Four noncoplanar points. wo opposite rays. wo intersecting lines 5. he intersection of plane LN and plane QL L P N U X Find the length of the segent.. P N 9. 8 P N Find the easure of the angle. 0. DBE. FBC. BF. DB F E 5 50 B D C. efer to the diagra for Exercises 0. Nae an obtuse angle, an acute angle, a right angle, and two copleentary angles. 5. Q is between P and. PQ = w º, Q =+w, and P =. Find the value of w. hen find the lengths of PQ and Q.. has endpoints (º, 8) and (, ). Find the coordinates of the idpoint,, of. hen use the Distance Forula to verify that =. 7. Use the diagra. If = 8, find the easures of 5 and. 8. uppose PQ = 0. If Q bisects PQ, what is the easure of PQ? he first five figures in a pattern are shown. Each suare in the grid is unit ª unit. 9. ake a table that shows the distance around each figure at each stage. 0. Describe the pattern of the distances and use it to predict the distance around the figure at stage 0. 5 center pivot irrigation syste uses a fixed water supply to water a circular region of a field. he radius of the watering syste is 50 feet long. (Use π..). If soe workers walked around the circuference of the watered region, how far would they have to walk? ound to the nearest foot.. Find the area of the region watered. ound to the nearest suare foot. 5 5 Chapter Geoetry English-panish eviews

2 8 In Exercises, solve the proportion. x. =. 8 5 z =. = 9 y Coplete the sentence.. If 5 = a b, then 5 a =? If b x = y, then 8 + x =? x y. In Exercises 8, use the figure shown.. Find the length of EF. 7. Find the length of FG. 8. Is uadrilateral FECB siilar to uadrilateral GFB? If so, what is the scale factor? In Exercises 9, use the figure shown. D.8. C. B..5.5 E F G.5 9. Prove that Q ~ Q. 0. What is the scale factor of Q to Q? 5 5. Is Q siilar to Q? Explain. 0. Find the length of Q. In Exercises 5, use the figure shown to decide if you are given enough inforation to conclude that JK L. If so, state the reason. LJ. J H = K KH L. HJK HL 5. L H H = JH KH H J K. he triangle is apped onto by a dilation with =, =, = 0, and =. Find the scale factor k, and side lengths and. 7. wo sides of a triangle have lengths of inches and 8 inches. he easure of the angle included by the sides is 5. wo sides of a second triangle have lengths of 7 inches and 8 inches. he easure of the angle included by the sides is 5. re the two triangles siilar? Explain. 8. You shine a flashlight on a book that is 9 inches tall and inches wide. It akes a shadow on the wall that is feet tall and feet wide. What is the scale factor of the book to its shadow? Not drawn to scale 9 in. ft 0 Chapter 8 Geoetry English-panish eviews

3 7 In Exercises, use the diagra. y. Identify the transforation XYZ. Y. Is congruent to XZ?. What is the iage of? X Z x. What is the preiage of Y? 5. ketch a polygon that has line syetry, but not rotational syetry.. ketch a polygon that has rotational syetry, but not line syetry. Use the diagra, in which lines and n are lines of reflection. 7. Identify the transforation that aps figure onto figure. 8. Identify the transforation that aps figure onto figure fl. 9. If the easure of the acute angle between and n is 85, what is the angle of rotation fro figure to figure fl? " n ' In Exercises 0, use the diagra, in which k. 0. Identify the transforation that aps figure onto figure. k. Identify the transforation that aps figure onto figure fl.. If the distance between k and is 5 units, what is the distance between corresponding parts of figure and figure fl?. What type of transforation is a coposition of a translation followed by a reflection in a line parallel to the translation vector? Give an exaple of the described coposition of transforations.. he order in which two transforations are perfored affects the final iage. 5. he order in which two transforations are perfored does not affect the final iage. FLG Identify any syetry in the flag. ' ". witzerland 7. Jaaica 8. United Kingdo Nae all of the isoetries that ap the frieze pattern onto itself Chapter 7 Geoetry English panish eviews

4 . ketch a concave pentagon. Find the value of each variable... 5x. y x x y x x y Decide if you are given enough inforation to prove that the uadrilateral is a parallelogra.. Diagonals are congruent. 7. Consecutive angles are suppleentary. 8. wo pairs of consecutive angles are congruent. 9. he diagonals have the sae idpoint. Decide whether the stateent is always, soeties, or never true. 0. rectangle is a suare.. parallelogra is a trapezoid.. rhobus is a parallelogra. What special type of uadrilateral is shown? Justify your answer efer to the coordinate diagra at the right. Use the Distance Forula to prove that WXYZ is a rhobus. hen explain how the diagra can be used to show that the diagonals of a rhobus bisect each other and are perpendicular. 8. ketch a kite and label it BCD. ark all congruent sides and angles of the kite. tate what you know about the diagonals C and BD and justify your answer. Y( a, 0) y X(0, b) W(a, 0) Z(0, b) x 9. PLN ND You want to build a plant stand with three eually spaced circular shelves. You want the top shelf to have a diaeter of inches and the botto shelf to have a diaeter of 5 inches. he diagra at the right shows a vertical cross section of the plant stand. What is the diaeter of the iddle shelf? in. x in. 5 in. 0. HIP OOF he sides of a hip roof for two trapezoids and two triangles, as shown. he two sides not shown are congruent to the corresponding sides that are shown. Find the total area of the sides of the roof. 7 ft ft 5 ft ft 0 ft 0 Chapter Geoetry English-panish eviews

5 In Exercises, identify all triangles in the figure that fit the given description.. isosceles. euilateral. scalene. acute 5. obtuse. right 7. In BC, the easure of is. he easure of B is three ties the easure of C. Find B and C. P Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which congruence postulate or theore you would use. Explain your reasoning. 8. B 9. H J 0. E N C D F G K L P. U. X. G H V W Z Y K J Find the value of x.. 5. x. x 70 x x x 5 POOF Write a two-colun proof or a paragraph proof. 7. GIVEN BD EC, C D 8. GIVEN XY WZ, XZ WY POVE B E POVE X W X Y B C D E Z W Place the figure in a coordinate plane and find the reuested inforation. 9. right triangle with leg lengths of units and 0. suare with side length s and vertices at 7 units; find the length of the hypotenuse. (0, 0) and (s, s); find the coordinates of the idpoint of a diagonal. 0 Chapter Geoetry English-panish eviews

6 In Exercises, identify the relationship between the angles in the diagra at the right.. and. and. and. and 5 5. and. 5 and 5 7. Write a flow proof. 8. If l, which angles are GIVEN = = 7, B fi BC suppleentary to? POVE = l B C n Use the given inforation and the diagra at the right to deterine which lines ust be parallel and are right angles.. 5; 5 and 7 are suppleentary. l n 5 7 p In Exercises and, write an euation of the line described.. he line parallel to y = º x + 5 and with a y-intercept of. he line perpendicular to y = ºx + and that passes through the point (º, ). Writing Describe a real-life object that has edges that are straight lines. re any of the lines skew? If so, describe a pair. 5. carpenter wants to cut two boards to fit snugly together. he carpenter s suares are aligned along EF as shown. re B and CD parallel? tate the theore that justifies your answer.. Use the diagra to write a proof. GIVEN, POVE n p l, 5 n p ndf 5 Chapter Geoetry English-panish eviews

Prove Theorems about Lines and Angles

Prove Theorems about Lines and Angles GEOMETRY Prove Theores about Lines and Angles OJECTIVE #: G.CO.9 OJECTIVE Prove theores about lines and angles. Theores include: vertical angles are congruent; when a transversal crosses parallel lines,