Honors Geometry Review Packet ) List all pairs of congruent angles.

Transcription

1 Honors Geometry Review Packet 2015 Note: Exam will include problems from that are not included on this packet PQR ~ CDE. 1) List all pairs of congruent angles. 2) Write the ratios of the corresponding sides in a statement of proportionality. In the diagram, ABCDE ~ FGHJK. 3) Find the value of x. 4) 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)

2 9) In Exercises 10 and 11, find the length of AB. 10) 11) Find the value of x. 12)

3 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? 15) A cellular telephone tower casts a shadow that is 24 meters long, while a tree nearby that is 9 meters tall casts a shadow that is 2 meters 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)

4 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? 18) You take 450 U.S. dollars to the bank to exchange for European euros. The exchange rate on that day is about 0.82 euros per U.S. dollar. How many European euros did you get for the 450 U.S. dollars? Short Answer: Answer the following questions completely. 19) If two polygons are congruent, must they be similar? If two polygons are similar, must they be congruent? Explain your answer. 20) Explain why all equilateral triangles are similar. Include sketches in your answer. 21) Explain how the side lengths of a triangle can be used to classify it as acute, right, or obtuse.

5 22) Explain why the acute angles in an isosceles right triangle always measure 45 o. 23) Explain when to use a trigonometric ratio to find a side length of a right triangle and when to use the Pythagorean Theorem. Find the value of x. Write your answer in simplest radical form. 24) 25) Classify the triangle as acute, right, or obtuse. 26) 3,5, 34 27) 9,15,10 3 Find the exact value of x. 28) 29)

6 Find the value of each variable. Keep your answer in simplest radical form. 30) 31) Solve the right triangle. Round your answer to the nearest tenth. 32) 33)

7 34) A balloon rises to the ceiling of a gymnasium. You want to find the distance from the ground to the balloon. You use a cardboard square to line up the balloon and the ground. Your friend measures the vertical distance from the ground to your eye and the distance from you to the gym wall. Approximate the distance from the ground to the balloon. 35) A soccer ball is placed 10 feet away from the goal, which is 8 feet high. You kick the ball and it hits the crossbar along the top of the goal. What is the angle of elevation of your kick? 36) The shadow of a telephone pole is 20 feet long. You measure the angle of elevation from the end of the shadow to the top of the telephone pole to be 70. What is the height of the telephone pole? Round your answer to the nearest foot.

8 Find the sum of the measures of the interior angles of the indicated convex polygon. 37) Decagon 38) 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. 39) ) 3960 Find the value of x. 41) 42) 43) 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.

9 Find the value of x in the parallelogram. 44) 45) Find the value of x. 46) 47) Give the most specific name for the quadrilateral. 48) 49) 50)

10 51) In the kite shown, m ADC = 105 and m DAB = 100. Find m DCB. Short Answer: Answer each question fully with complete sentences. 52) Explain why any two regular pentagons are similar. 53) In parallelogram ABCD, the measure of angle A is 65 degrees. Explain how you would find the other angles measures of parallelogram ABCD. 54) A quadrilateral has four congruent sides. Is the quadrilateral a parallelogram? Justify your answer. 55) The diagonals of a rhombus are 6 inches and 8 inches. What is the perimeter of the rhombus? Explain. 56) Explain why a parallelogram with one right angles must be a rectangle.

11 Tell how many common tangents the given circles have. Then draw the common tangents. 57) 58) QR is a radius of R and PQ is tangent to R. Find the value of x. 59) 60) 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. 61) mkln 62) mjnl 63) mlm

12 Find the measure of the given arc. 64) mac 65) mqrs Find the value(s) of the variable(s). 66) 67) 68) 69)

13 70) 71) 72) Write the standard equation of a circle with a center of (-5, 4) and has a radius of 6. 73) Write the standard equation of a circle that has a center of (4, 8) and a point on the circle of (6, 2). 2 74) Graph the equation 2 x y

14 Use the diagram to find the indicated measure. 75) Find the circumference. A = 17.64π m 2 76) Find the radius. C = 100 ft Find the indicated measure. Round answers to the nearest tenth. 78) Length of AB 79) Circumference of L The area of D is square meters. The area of sector ADB is 34.6 square meters. Find the indicated measure. 80) Radius of D 81) Circumference of D 82) m AB 83) Length of ACB

15 Find the area of the shaded region. Round answers to the nearest tenth, if necessary. 84) 85) 86) 87) Find the probability that a randomly chosen point in the figure lies in the shaded region. 88)

16 89) 90) A measuring wheel is used to calculate the length of a path. The diameter of the wheel is 8 cm. The wheel rotates 87 times along the length of the path. About how long is the path? 91) The area of a circular pond is about 138,656 square meters. You are going to walk around the entire edge of the pond. About how far will you walk? Give your answer to the nearest meter. 92) Basaltic columns are geological formations that result from rapidly cooling lava. The Giant s Causeway in Ireland contains many hexagonal columns. Suppose that one of the columns is in the shape of a regular hexagon with radius 8 inches. What is the apothem of the column? Find the perimeter and area of the column. Round the area to the nearest square inch.