For all questions, means none of the above answers is correct. Diagrams are NOT drawn to scale.. In the diagram, given m = 57, m = (x+ ), m = (4x 5). Find the degree measure of the smallest angle. 5. The measure of a supplement of an angle is four times the measure of the complement of the angle. Find the measure of the complement. A. 0 B. 40 C. 60 D. 80 6. In the diagram, a b, c d, m = x+ 0, m = y 5, m = x+ 50, m 4= x+ y. Find the value of x+ y. A. 8 B. 56 C. 57 D. 58. In the diagram, given m = 6, m = (x+ ), m = (x+ ). Find the degree measure of. A. 4.5 B. 8.75 C..5 D. 40.5. Which statement is true for ALL parallelograms? A. The diagonals are perpendicular to each other. B. The diagonals are congruent. C. The diagonals bisect opposite angles. D. The diagonals bisect each other. 4. Quadrilateral ABCD is a parallelogram. Given: AB = x + 5, BC = x, CD = y 5, AD = y. Determine the length of AB. A. 0 B. 5 C. 0 D. 5 A. 5 B. 5 C. 70 D. 85 7. Which of the following statements is FALSE? A. Two planes perpendicular to the same line at different points of the line are parallel. B. If two lines are parallel, a plane containing one and only one of them is parallel to the other line. C. Two lines perpendicular to the same line are parallel to each other. D. If two parallel planes are cut by a third plane, then the lines of intersection are parallel. 8. In the figure, AB = BC = CD = ED = EF =. Find the length of AF. A. B. C. 6 D. 5
9. In ΔABC, E is a point on AC, D is a point on ABsuch that ED CB. AB = x, EC = 5, AD = 6, BD = x + 7, and ED = 7. Find the perimeter of Δ ABC. A. 4 B. C. 5 54 6 5. Which is the longest segment in the diagram given m D = 90, m CAD = 60, m CAB = 4, m ACB = 86. D. 5 6 6 0. In parallelogram ABCD, AB = 4 x, BC = 6x + 5, AD = 4x + 5. Find the numerical perimeter of ABCD. A. 5 B. 0 C. 90 D. 05. In Δ XYZ, XY = 8, YZ = 40, XZ = 4. A. The triangle is acute. B. The triangle is right. C. The triangle is obtuse. D. No triangle possible with these side lengths.. ΔABC is a right triangle with hypotenuse AB. D is a point on the hypotenuse such that CD If AD = 6, BD = 9, find the length of AC. A. 4 B. C. 5 D. 0 AB.. Point X is equidistant from vertices T and N of Δ TEN. Point X must lie on which of the following? A. perpendicular bisector of TN B. bisector of E C. median to TN D. the altitude to TN 4. Find the perimeter of a rhombus with diagonals having lengths 4 and. A. 40 B. 56 C. 7 D. 80 A. CD B. CB C. BA D. AC 6. In Δ ABC, D is a point on AC such that ray BD bisects ABC. Find the length of AD when AB = 7. BC = 9, and AC = 8. A. 7 B. 9 C. 56 9 D. 6 8 7. Given the diagram with angles as labeled and x w= 0, find the value of y z. A. 0 B. 0 C. 0 D. 0 8. The sum of the measures of the interior angles of a convex polygon is 880. How many diagonals does this polygon have? A. 04 B. 9 C. 5 D. 88 9. Given parallelogram ABCD with m B = 60, AD =, CD = 8. Find the length of the altitude to AD. A. 6 B. 9 C. 9 D.
0. Given the triangle with angles as marked, what is the value of x in terms of y? A. 60 B. 80 C. 00 + y D. 80 y. The supplement of the complement of an acute angle is always A. an acute angle B. an obtuse angle C. a straight line D. a right angle. In isosceles Δ ABC x is the degree measure of the vertex angle B and y is the degree measure of the exterior angle at B. Find the degree measure of Ain terms of x and/or y. A. x B. 90 y C. 80 y D. y. If V is the measure of an exterior angle of a regular polygon and 50 < V < 55, how many sides does the polygon have? A. 5 B. 7 C. 9 D. 4. In quadrilateral ABCD, diagonals AC and BD are drawn. ΔADB is equilateral with AD = 6, BC = CD = 5. Find the length of AC. A. 7 B. 4+ C. 4+ D. 0 5. In rectangle ABCD, the lengths of the sides are 4 and 8. Find the perimeter of the convex quadrilateral formed by joining the midpoints of the rectangle consecutively. A. 5 B. 0 C. 60 D. 84 6. ABCD is a square, and ABE is an equilateral triangle with E a point in the exterior of the square. Find the m AED in degrees. A. 0 B. C. 5 D. cannot be determined 7. ΔABC is a right isosceles triangle with right angle C. D is a point on ABand E is a point on AC such that DE BC. If AD =, EC =, find the value of AC + DB + DE. A. B. + C. 5+ D. 5 8. In right triangle ABC with right angle at A, CB =, AC =. Find the value of cos C sin B. A. B. C. D. 5 9. In ΔABD, AC is the altitude to BD, AC is a median, and BAC is complementary to D. Which of the following statements is false? A. BAC DAC B. BAC and B are complementary C. BAD is a right angle D. ΔABD is isosceles 0. A dog walks miles north, miles east, 5 miles north and mile west. What is the shortest distance from his starting position? A. 5 B. C. 5 D. 65
SOLUTIONS. B 7. C. A 9. C 5. C. C 8. E 4. D 0. E 6. C. D 9. D 5.C. B 7. B 4. D 0. E 6.A. D 8. A 5. A. C 7. A. B 9. C 6. D. D 8. C 4. C 0. C. B The sum of the angles is 80 giving 7x+ 54 = 80, x = 8. m = 56, m = 67.. C m + m = m, x+ 66 = 6x+ 9, 57 Substituting + = 4. D A is true in rhombuses and squares. B is true in squares and rectangles. C is true in rhombuses and squares. 57 x =. 4 4. D Opposites sides are congruent therefore: y=, x x+ 5= y 5. Solve this system to get x= 0, y= 0. AB = 5. 5. A 80 x 4( 90 x) =, x = 60, complement is 0, supplement is 0. 6. C 7. C The lines must be in the same plane for this to be true. 8. E Since each triangle is a right triangle and you always know the legs, use the Pythagorean Theorem 4 times to get 5. 9. D The triangles are similar by AA. First, solve for xx. + 7 + 6 = x, x=. Now use proportions to solve for AE. 6 AE, = AE = And use proportions 0 5. 7 6 to solve for CB, = BC = 0. Add the BC 6, following to get the perimeter: 5 5 + + 6 + 0 + 0 = 6. 6 0. E Since this is a parallelogram, opposites sides are congruent making 4x+ 5 = 6x+ 5, x = 5. AB = DC = 0, BC = AD = 5 making the perimeter 0.. C 4 > 40 + 8 so the triangle is obtuse.. D The three triangles formed are similar so using the geometric mean formulas, AC = AD AB = 6 5 = 0.. A By theorem. 4. D Diagonals are perpendicular and bisect each other in a rhombus. So one of the triangles formed has legs of and 6 making the hypotenuse which is a side of the rhombus 0. The perimeter is 80. 5. C In triangle ACD, AC is longest since it is opposite a 90 degree angle. In ABC, AB is longest since it is opposite an 86 degree angle. 6. A Using the triangle angle bisector theorem, 7 9 x = 8 x, 7 x =. 7. A Since the vertical angles are congruent, the sum of the other two angles in each triangle are equal. x+ y = z+ w. Since we want y z, rearrange the equation to get y z = w xand x w= 0, so z y = ( x w), or 0. 8. C First, find the number of sides of the polygon. n 80= 880, n= 8. Then find the number of ( ) diagonals 8 5 = 5.
9. C Draw the altitude from C to AD. This forms a 0 60 90 triangle with a hypotenuse of 8. The altitude is opposite a 60 angle making the altitude 9. z = x+ 50, y+ z+ 0 = 80, z = 50 y, 0. E 50 y = x+ 50,00 y = x.. B The complement and the angle must both be acute making the supplement obtuse.. D Since the base angles are congruent and must add up to the exterior angle at the vertex angle, each must be y.. B To solve this, look at regular polygons and the measure of one exterior angle. # sides Exterior angle 0 4 90 5 7 6 60 60 7 = 5 7 7 7. B These two triangle are similar by AA. And both are isosceles right triangles. Since AD =, AE + DE =. Using proportions, AD AE =, =, BD =. BD EC BC AC + DB + DE = + + + = + 8. A cosc sin B = = or remember that the cosine of one angle is the sine of the other. 9. C All the others can be proved true since the two triangles are congruent. 0. C The right triangle formed by connecting the ending point with the beginning point has legs of 7 and. 7 + = 5. 4. C This is a kite by definition. So the diagonals are perpendicular and one of them is bisected. Let E be the point of intersection of the diagonals. DE = EB = making AE = and EC = 4. AC = 4 +. 5. C Use Pythagorean Theorem to find the diagonals are 0. Sides of the quadrilateral formed by connecting the midpoints are the diagonals. The perimeter is 60. 6. C m DAE = 90 + 60 = 50. Since ΔADE is isosceles, ADE AED so each is 80 50 = 5.