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Name _______________________________________ Date ___________________ Class __________________ Project Problems Set 2 Module 4 1. The polygon Q(3, 2), R(6, 5), S(6, 2) undergoes the transformation: (x, y) (4x, 4y). Name the coordinates of the image points. 8. In the figure, PQR UVW. What is mR? 2. The angles of a triangle measure 4, 86, and 90. Which classification of the triangle is correct? 3. Which could be the angle measures of an acute triangle? A 32-56-92 C 34-56-90 B 33-58-91 D 35-56-89 4. What is the length of the longest side of the triangle? 5. What is mW ? 6. Two angles of a triangle measure 22 and 53. What is the measure of the third angle? 7. What is the value of x if the acute angles of a right triangle measure 8x and 12x? 9. If KMQ WJR, which segment is congruent to RW ? 10. Which angle is congruent to Z if ZLV SPN ? 11. If ABC KJC, which statement is NOT necessarily true? 12. Suppose S N, J I, A T, JS IN, JA IT , and AS TN. Write a congruency statement for the two triangles. 13. The transformation M: (x, y) (0.5x, 0.5y) has been applied to the polygon KLM. If the point M had coordinates (4, 4), name the coordinates of the image of M. ________________________________________ 14. Is the polygon K(5, 4), L(5, 6), M(7, 6) congruent to the polygon N(4, 3), P(4, 5), Q(6, 5)? ________________________________________ Use the figure for Exercises 15 and 16. 15. Classify the triangle by its angle measures. ________________________________________ 21. Complete the statement. Two triangles are congruent if and only if their _______ angles and sides are congruent. ________________________________________ Use the figure for Exercises 22 and 23. 22. What value of x proves ABC DEF by SAS? ________________________________________ ________________________________________ 16. Classify the triangle by its side lengths. ________________________________________ 17. Complete the sentence. All of the angles in an equilateral triangle measure _________. 23. If AB DE , what additional congruence statement is needed to prove ABC DEF by SSS? ________________________________________ Use the figure for Exercises 24 and 25. ________________________________________ 18. What is the measure of 1? 24. Write True or False. You can use AAS to prove ABE CDE. ________________________________________ ________________________________________ 19. Given: GHJ NOP. What is the value of x? ________________________________________ 20. If KLM RST, what is the value of x? 25. What additional congruence statement is needed to prove ABE CDE by HL? Module 5 1. If x= 5 is RST UVW ? Explain. 6. When using HL congruence theorem, what type of triangles do you need? 7. Find the value of x. . 2. What additional information is needed to prove MNP PQM by SAS? 8.What is the measure of one of the base angles of an isosceles triangle if the measure of the vertex angle is 98? 9. One angle of an equilateral triangle measures (4x 20). What is the value of x? 3. A parachute jumper called into the airport to be rescued by helicopter. She said her pilot flew 8 kilometers west and then headed due north about 20 minutes before she jumped. Does the helicopter pilot have enough information to locate her exact location? Explain. 10. Suppose MWR CYQ, MW 8, WR 9, and CQ 10. What is MR? F 8 H 10 G 9 J 11 11. Write True or False and explain. 4. Which congruence theorem CANNOT be used to prove MNK KLM? 5.In the figure, H is the midpoint of EK and FJ . What reason can be used in a proof to show EF JK ? Given: ABC and DEF. To use CPCTC to prove A D, you must first prove ABC DEF. 12. What postulate or theorem proves K M? Module 8 1. Which is similar to this quadrilateral? A C B D 6. The scale on a map uses 3 centimeters to represent 4 kilometers. The distance between two towns on the map is 6 centimeters. How many kilometers apart are the towns? 7. The coordinates of PMN are P(2, 10), M(8, 6), and N(4, 2). After a dilation, the image of P is (19, 95). What are the coordinates of the image of M? 2. Complete the similarity statement. 8. Determine whether the triangles are similar. If so, write the similarity ratio and a similarity statement. ABC ? 3. The dilation D: (x, y) (0.2x, 0.2y) has been applied to the polygon S(–5, 5), T(–5, 10), U(5, 15). What are the coordinates of the image points? 4. Which transformation(s) can be used to show that polygon W(–2, 4), X(–2, 8), Y(–6, 2), Z(–10, 4) is similar to polygon L(–3, 0), M(–3, 2), N(–5, –1), O(–7, 0)? 5. To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. What is AB to the nearest meter? 9. Give the definition of a dilation. 10. Name the dilation and then the translation that was used to map O(2, 5), P(6,1), Q(0, –1), R(–1, 0) to A(8, 14), B(16, 6), C(4, 2), D(2, 4). 11. Given that UOV is a dilation image of SOT, find the coordinates of V and the scale factor. 11