FINAL EXAM REVIEW CH Determine the most precise name for each quadrilateral.

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1 FINAL EXAM REVIEW CH 6 1. Determine the most precise name for each quadrilateral. 2. Find the measures of the numbered angle for the following parallelogram a. A(-5,7), B(2,6), C(-4,0), D(5,-3) True or False 4. Find the measures of the numbered angle for the following rhombus If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram Show TTTT RRRR 6. Fill in the blank of the following statement TT(dd, yy) RR(xx dd, yy) A is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent PP(0,0) AA(xx, 0) 7. Find the value of the variables for which ABCD must be a parallelogram BB xx zz CC 8. Find the value of the variables for which ABCD must be a parallelogram BB 4xx 4 2xx CC 2yy + 2 3xx + 2 AA 57 yy DD AA DD

2 FINAL EXAM REVIEW CH 6 9. Find the length of the legs of the isosceles triangle (bb, 2cc) 10. GIVEN: Kite JERK with JJJJ RRRR and JJJJ RRRR PROVE: JJ RR JJ KK EE (2bb, 0) RR 11. GIVEN: Triangle MNO is a right triangle with right MMMMMM. P is the midpoint of MMMM PROVE: OOOO = 1 MMMM Give the coordinates for points W and Z in the following square. MM(0,2aa) WW (bb, bb) PP ZZ (bb, bb) OO NN(2bb, 0) 13. GIVEN: Trapezoid TTTTTTTT with TTTT PPPP and D, E, F, and G are midpoints PROVE: DD, EE, FF, aaaaaa GG form a rhombus 14. GIVEN: AAAAAAAA is a parallelogram. AAAA bisects BBBBBB and BBBBBB PROVE: AAAAAAAA is a rhombus RR(-2b, 2c) EE AA(2bb, 2cc) AA 3 4 DD DD FF TT( 2aa, 0) GG PP(2aa, 0) BB 2 1 CC 15. GIVEN: Trapezoid ZZZZZZZZ with parallelogram ZZZZZZZZ and DD II PROVE: ZZZZ OOOO 16. Determine whether the quadrilateral must be a parallelogram. ZZ OO DD MM II

3 FINAL EXAM REVIEW CH Find the geometric mean of 3 5 and 5 in simplest radical form. 2. In the diagram above, WWWW YYYY aaaaaa XXXX ZZZZ ; Find the perimeter of XXXXXX 3. Find the value of xx 3xx + 5 xx + 3 = 15 9 xx 4. Determine if the triangles are similar and write a similarity statement 5. Find the value of each variable. Leave your answer in simplest radical form if not a whole number. 6. Find the value of each variable. Leave your answer in simplest radical form if not a whole number. 7. Kevin wishes to measure the height of a flagpole using a mirror. His eye is 1.68m above the ground. If he places the mirror 5.7m from the base of the flagpole, and he has to back away 114 cm from the mirror to see the top of the flagpole, how tall in is the flagpole? 8. Find the value of xx.

4 FINAL EXAM REVIEW CH Find the value of xx. (use the quadratic formula). xx 1 = xx + 1 xx 10. The area of an isosceles triangle is 36 square inches. The ratio of the length of the triangle s base to its height is 3:1. What is the perimeter of the triangle?

5 FINAL EXAM REVIEW CH 8 1. Write the expression in simplest radical form Express ssssss AA, cccccc AA aaaaaa tttttt AA as ratios, simplify if possible. 3. The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse, or right. 13, 21, Two hills are two miles apart. The taller hill is 2707ft high. The angle of depression from the top of the taller hill to the top of the shorter hill is 7. Find the height of the shorter hill to the nearest foot (1 mi = 5280 ft.) 5, 4, 3 5. Find area of the largest pentagon 6. Find the value of xx to the nearest tenth.

6 FINAL EXAM REVIEW CH 8 7. In problems 7-9, find the area of the given shapes. 8. Find the area of a regular hexagon with side length of 8cm. 9. Write the expression in simplest radical form Find the exact length of each missing side. 11. A surveyor is 305 ft. from the base of the new courthouse. Her angle measuring device is 5 ft. above the ground. The angle of elevation to the top of the courthouse is 42. Find the height of the courthouse to the nearest foot. 12. Write the expression in simplest radical form

7 FINAL EXAM REVIEW CH 9 AND In problems 1-3, find the area of each shaded sector of the circle In the figure to the left, if a dart hit the board, find the probability that it will land in regionzz. 5. A dilation with scale factor 4 maps square A onto square B. The area of square B is 25. Find the area of square A.

8 FINAL EXAM REVIEW CH 9 AND Find the coordinates of the image of each set of points for a dilation with center MM and the scale factor given. MM( 3,4), AA( 6, 1), HH(3,2); ssssssssss ffffffffffff 4 8. Find a single translation that has the same effect as each composition of translations (xx, yy) (xx + 3, yy + 5.2) ffffffffffffffff bbbb (xx, yy) (xx + 1.2, yy + 6) Find the image of AA(0,0) SS(3,2) KK(0,3) after two reflections, first across ll 1 then across ll 2 9. ll 1 : yy = 1; ll 2 : xx = ll 1 : yy = xx; ll 2 : xx aaaaaaaa 11. Find the exact area of the following shape 12. Find the exact area of the shaded region

9 FINAL EXAM REVIEW CH In problems 1-3 find the SURFACE AREA and VOLUME of the given figures A square pyramid resting on its base is filled to half its height with 320 cm of water. How much water is needed to finish filling the pyramid? 5. The volume of the solid is 360 fftt 3 find the value of xx. 6. The solid below is a peg with a square hole. Find its surface area. 7. Find the volume and surface area.

10 FINAL EXAM REVIEW CH Find the volume of the solid of revolution rotated about the yy = Find the total surface area of the solid of revolution found by rotating the triangle about the vertical line. 9. Find the volume and surface area. 10. The slant height of a square pyramid is 6 more than the length of a side of the base. The surface area of the pyramid is 231 centimeters. Find the slant height and the length of a side of the base of the pyramid. 11. Paul just discovered that the valve on his cement truck (why he has a cement truck I don t know), failed during the night and that all the contents ran out to form a giant cone of hardened cement. To make an insurance claim, Paul needs to figure out how much cement is in the cone. The circumference of its base is 44 feet and it is 5 feet high. Calculate the volume. 12. Find the surface area.

11 FINAL EXAM REVIEW CH Find the value of each variable given the following chords and tangents. 2. AAAA is tangent to circle CC at BB. Find the value of xx. 3. Find the radius and center of the given circle 4. Find the radius and the mmaaaa yy 2 + 7xx + xx 2 5yy 10 = 0 5. Find the value of xx. 6. ZZZZ is tangent to circle OO and PP. Find the value of xx. xx Find the value of the variables given the following chords and secants. 8. Find the value of xx.

12 FINAL EXAM REVIEW CH Find the value of xx. 10. Find the value of the variable given the following chords, secants and tangent.