2) Find the value of x. 8

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1 In the figure at the right, ABC is similar to DEF. 1) Write three equal ratios to show corresponding sides are proportional. D 16 E x 9 B F 2) Find the value of x. 8 y A 16 C 3) Find the value of y. Determine whether the triangles are similar. If so, write a similarity statement and the postulate or theorem that justifies your answer. 4) 5) Determine the value of x that makes ΔABC ~ ΔXYZ. 7)

2 8) In Exercises 9 and 10, find the length of AB. 9) 10) Find the value of x. 11)

3 12) The panels in the sail are parallel. Find the length of x and y. 13) A cellular telephone tower casts a shadow that is 72 feet long, while a tree nearby that is 27 feet tall casts a shadow that is 6 feet long. How tall is the tower? 14) You are making a scale model of your school s baseball diamond as part of an art project. The distance between two consecutive bases is 90 feet. If you use a scale factor of 1/180 to build your model, what will be the distance around the bases on your model? 15) Laura and Will are sitting on opposite sides of a 12 foot seesaw. The fulcrum (support) at the center is 3 feet high. When Laura s end of the seesaw is touching the ground, how many feet off the ground is Will s end of the seesaw?

4 16) Draw a polygon with the given vertices. Then draw a dilation of the polygon using the given scale factor k. A( 1, 1), B(2, 1), C(1, 2); k = 3 Short Answer: Answer two of the following questions completely. 17) If two polygons are congruent, must they be similar? If two polygons are similar, must they be congruent? Explain your answer. 18) Explain why all equilateral triangles are similar. Include sketches in your answer. 19) List the three ways we learned in this chapter to show that triangles are similar. 1) Tell whether the given side lengths of the triangle can represent a right triangle. 9, 12, 15

5 2) What is the length of the hypotenuse, c, of the following right triangle? a = 15; b = 20; c =? 3) Simplify completely ) Simplify completely ) A ladder is leaning against the side of a 24 m house. If the base of the ladder is 7 m away from the house, how tall is the ladder? Draw a diagram and show all work. 1) Find the geometric mean of 9 and 4. 2) 15 is the geometric mean of 25 and what other number? Solve for the missing variable. 3) 4)

6 5) 1) Solve for the value of x. Round to the nearest tenth. 2) Solve for the value of x. Round to the nearest tenth. 3) Solve for the value of x. Round to the nearest tenth. 4) Solve the right triangle. Round decimal answers to the nearest tenth. C 5 B 13 A

7 Find the sum of the measures of the interior angles of the indicated convex polygon. 1) Decagon 2) 18-gon The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides. 3) ) 3960 Find the value of x. 5) 6) 7) Trapezoid ABCD. Show all work. m Bis three times m C. Find m Band m C. A B D C

8 Find the value of the variables in the parallelogram. 8) 9) 10) 11) Find the length of the midsegment of the trapezoid. Find the value of x. 12) 13)

9 Refer to kite PQRS with PQ = QR = 10, PR = 16, RS = 12 14) TR = Q P T R 15) TS = 16) If m QRT 40 o, then m QRT S 17) List five properties of parallelograms. 18) List the properties of a square that are not properties of every rectangle. 19) List three properties of a rhombus that are not properties of every parallelogram. Tell how many common tangents the given circles have. Then draw the common tangents. 1) 2)

10 QR is a radius of R and PQ is tangent to R. Find the value of x. 3) 4) JM and KN are diameters of P. Identify the given arc as a major arc, minor arc, or semicircle. Then find the measure of the arc. 5) mkln 6) mjnl 7) mlm Find the measure of the given arc. 8) m AC 9) mqrs Find the value(s) of the variable(s).

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12 15) If a circle is circumscribed about a polygon, then the polygon is in the circle. 16) If ACB and DCE are congruent central angles of C, then ABand DE are. 17) The points A and B are on C. If C is a point on AB, then AB is a. 18) If a chord passes through the center of a circle, then it is called a(n). 19) A is a line that intersects a circle in two points. 20) A is a line that intersects a circle in exactly one point. Questions from Area and Circumference of circles Area of polygons