2 nd Semester Geometry Review Packet. In the diagram, ABCDE ~ FGHJK. 1) Find the value of x. 2) Find the perimeter of ABCDE.

Transcription

1 In the diagram, ABCDE ~ FGHJK. 1) Find the value of x. 2) Find the perimeter of ABCDE. Determine whether the triangles are similar. If so, write a similarity statement and the postulate or theorem that justifies your answer. 6) 7) Determine the value of x that makes ΔABC ~ ΔXYZ. 8) 9) In Exercises 10 and 11, find the length of AB.

2 10) 11) Find the value of x. 12) 13) The panels in the sail are parallel. Find the length of x and y. 14) The perimeter of a rectangular corn field is 440 meters. The ratio of its length to its width is 7:4. What is the length and width of the field?

3 15) 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? 16) Plot the coordinate on the coordinate plane and find coordinate for point E so that ABC ~ ADE. A(0, 0), B(0, 6), C(3, 0), D(0, 9), E(x, y) 17) 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? Short Answer: Answer the following questions completely. 18) If two polygons are congruent, must they be similar? If two polygons are similar, must they be congruent? Explain your answer. 19) Explain why all equilateral triangles are similar. Include sketches in your answer. 20) How can you show that two triangles are similar? Fill-in the blank with the most appropriate word to complete the sentence. 1) A set of three positive integers a, b, and c that satisfy the equation c a b is called a.

4 2) The longest side of a right triangle is called the. 3) Two triangles are if their corresponding angles are congruent and their corresponding side lengths are proportional. 4) A triangle with two congruent sides and a right angle is called an. Find the unknown side length. Write your answer in simplest radical form. 5) 6) 7) Classify the triangle formed by the side lengths as right,acute, or obtuse. 8) 4, 5, 6 9) 11, 13, 23 10) 8, 8 3, 16 11) Find the area of the isosceles triangle. 12) Find the geometric mean of 3 and 7. Solve for the missing variable(s). 13) x

5 15) 14) x y y x Find the value of each variable. Write your answers in simplest radical form. 16) ) 18) 23) In baseball, the distance of the paths between each pair of consecutive bases is 90 feet and the paths form right angles. How far does the ball need to travel if it is thrown from home plate directly to second base? Find the sum of the measures of the interior angles of the indicated convex polygon.

6 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) The measure of one interior angle of a parallelogram is 42 degrees more than twice the measure of another angle. Find the measure of each angle. Find the value of the variables in the parallelogram. 8) 9) 10) 11) Find the length of the midsegment of the trapezoid.

7 Find the value of x. 12) 13) Give the most specific name for the quadrilateral. Explain your answer. 14) 15) 16) 17) In the kite JKLM, find the measure of K.

8 18) Short Answer: Answer two questions fully with complete sentences. a) In parallelogram ABCD, the measure of angle A is 65 degrees. Explain how you would find the other angles measures of parallelogram ABCD. b) A quadrilateral has four congruent sides. Is the quadrilateral a parallelogram? Justify your answer. c) The diagonals of a rhombus are 6 inches and 8 inches. What is the perimeter of the rhombus? Explain. d) Explain why a parallelogram with one right angle must be a rectangle. Use the diagram to find the indicated measure. 1) Find the circumference. 2) Find the radius. C = 113 km Find the length of JK. Round answers to the nearest tenth. 3) 4)

9 Find the indicated measure. Round answers to the nearest tenth. Find the radius of circle L. 5) 6) Find the circumference of circle C. Find the area of the sector. Round to the nearest tenth. 7) 8) Find the area of the regular polygon. Round to the nearest tenth. 9)

10 10) A circle with a diameter of 10 in. contains an inscribed square as shown below. Find the area of the shaded region. Leave your answer in terms of π. 11) ) A circle has an 8 in. radius. Find the area of a sector whose arc measures 135. Leave your answer in terms of π. 13) How much more pizza is in a 12 in. diameter pizza than in a 10 in pizza? 14) Find the area of a regular pentagon with a 12.3 in. apothem and 8 in. sides.

11 15) A gazebo is built in the shape of a regular octagon. Each side is 8 ft long, and its apothem is 9.7 feet. To the nearest tenth, find the area enclosed by the gazebo. 16) If a dart randomly hits the board, what is the probability that it will hit in region II? I II 10 III IV Tell whether the solid is a polyhedron. If it is, find the number of faces, vertices, and edges. 1) 2) Use Euler s Theorem to find the value of n. 3) Faces: 8, Vertices: 12, Edges: n 4) Faces: 9, Vertices: n, Edges: 21 5) Faces: n, Vertices: 16, Edges: 24 Find the surface area and volume of the solid. The pyramids are regular and the prisms, cones, and cylinders are right. Round your answers to two decimal places, if necessary. 6)

12 17) Describe the shape that is formed by the cut made in the food shown. 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 14) The surface area of a lacrosse ball is approximately 20 square inches. What is the diameter of the ball? Tell how many common tangents the given circles have. Then draw the common tangents. 1) 2) QR is a radius of R and PQ is tangent to R. Find the value of x. 3)

13 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). 10) 11) 12)

14 13) 14) 15) 16) Write the standard equation of a circle with a center of (-5, 4) and has a radius of 6. 17) Write the standard equation of a circle that has a center of (4, 8) and a point on the circle of (6, 2). 2 18) Graph the equation x y