Exam 12: Geometry Problems: Complementary Angles, Collinear Points, and Similar Triangles

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Leaving home, the driver of a car travels 10 miles in the direction N 53° E. In what direction must the driver travel to return home?

(Multiple Choice)
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  -If   bisects   , then   . -If   -If   bisects   , then   . bisects   -If   bisects   , then   . , then   -If   bisects   , then   . .

(True/False)
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The lines which are the graphs of The lines which are the graphs of   and   intersect at one point. and The lines which are the graphs of   and   intersect at one point. intersect at one point.

(True/False)
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In In   ,   and   . If   , find   . , In   ,   and   . If   , find   . and In   ,   and   . If   , find   . . If In   ,   and   . If   , find   . , find In   ,   and   . If   , find   . .

(Multiple Choice)
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If the sides of If the sides of   have measures a = 3, b = 4, and c = 5, then the measure of   (the angle opposite the side of length c) is 90°. have measures a = 3, b = 4, and c = 5, then the measure of If the sides of   have measures a = 3, b = 4, and c = 5, then the measure of   (the angle opposite the side of length c) is 90°. (the angle opposite the side of length c) is 90°.

(True/False)
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  -If the diagonals of a rhombus measure 10 cm and 24 cm, what is the perimeter of the rhombus? -If the diagonals of a rhombus measure 10 cm and 24 cm, what is the perimeter of the rhombus?

(Multiple Choice)
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If midpoints are involved in a proof, then a general point should be represented by ( If midpoints are involved in a proof, then a general point should be represented by (   ). ).

(True/False)
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  -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . -Let   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . and   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . be a pair of adjacent angles for which m   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . = 37° and m   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . = 49°. If   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . bisects   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . and   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . bisects   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . , find m   -Let   and   be a pair of adjacent angles for which m   = 37° and m   = 49°. If   bisects   and   bisects   , find m   . .

(Short Answer)
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  -In the figure, A-C-D-B,   , and   . Of the line segments drawn from point P to   , which has the greatest length? -In the figure, A-C-D-B,   -In the figure, A-C-D-B,   , and   . Of the line segments drawn from point P to   , which has the greatest length? , and   -In the figure, A-C-D-B,   , and   . Of the line segments drawn from point P to   , which has the greatest length? . Of the line segments drawn from point P to   -In the figure, A-C-D-B,   , and   . Of the line segments drawn from point P to   , which has the greatest length? , which has the greatest length?

(Essay)
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The diagonals of any rhombus are perpendicular.

(True/False)
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  -For trapezoid HJKL,   . If   , then: -For trapezoid HJKL,   -For trapezoid HJKL,   . If   , then: . If   -For trapezoid HJKL,   . If   , then: , then:

(Multiple Choice)
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Find a direction vector for the line that contains the points Find a direction vector for the line that contains the points   and   . and Find a direction vector for the line that contains the points   and   . .

(Multiple Choice)
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  -In   , m   and m   . Determine the value of x. -In   -In   , m   and m   . Determine the value of x. , m   -In   , m   and m   . Determine the value of x. and m   -In   , m   and m   . Determine the value of x. . Determine the value of x.

(Short Answer)
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  -For trapezoid RSTV,   . If M is the midpoint of   and N is the midpoint of   , it follows that: -For trapezoid RSTV,   -For trapezoid RSTV,   . If M is the midpoint of   and N is the midpoint of   , it follows that: . If M is the midpoint of   -For trapezoid RSTV,   . If M is the midpoint of   and N is the midpoint of   , it follows that: and N is the midpoint of   -For trapezoid RSTV,   . If M is the midpoint of   and N is the midpoint of   , it follows that: , it follows that:

(Multiple Choice)
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It is given that It is given that   . If   ,   ,   , and   , find y. . If It is given that   . If   ,   ,   , and   , find y. , It is given that   . If   ,   ,   , and   , find y. , It is given that   . If   ,   ,   , and   , find y. , and It is given that   . If   ,   ,   , and   , find y. , find y.

(Essay)
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Diameter Diameter   of   is perpendicular to chord   at point E. If CD = 18 and OE = 5, find the length of   . of Diameter   of   is perpendicular to chord   at point E. If CD = 18 and OE = 5, find the length of   . is perpendicular to chord Diameter   of   is perpendicular to chord   at point E. If CD = 18 and OE = 5, find the length of   . at point E. If CD = 18 and OE = 5, find the length of Diameter   of   is perpendicular to chord   at point E. If CD = 18 and OE = 5, find the length of   . .

(Essay)
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  -For a right circular cylinder, the length of radius of base is 2.3 inches and the altitude measures 8.5 inches. Correct to the nearest tenth of cubic inch, find the volume of the cylinder. -For a right circular cylinder, the length of radius of base is 2.3 inches and the altitude measures 8.5 inches. Correct to the nearest tenth of cubic inch, find the volume of the cylinder.

(Essay)
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  -For the quadrilateral shown, variables a, b, and c are related by the equation   . Being as specific as possible, what type of quadrilateral is shown? -For the quadrilateral shown, variables a, b, and c are related by the equation   -For the quadrilateral shown, variables a, b, and c are related by the equation   . Being as specific as possible, what type of quadrilateral is shown? . Being as specific as possible, what type of quadrilateral is shown?

(Short Answer)
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  -In the figure,   is tangent to the circle at point T while   is a secant for the circle. -In the figure,   -In the figure,   is tangent to the circle at point T while   is a secant for the circle. is tangent to the circle at point T while   -In the figure,   is tangent to the circle at point T while   is a secant for the circle. is a secant for the circle.

(True/False)
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  -The three altitudes of an obtuse triangle are concurrent at a point that lies in the exterior of that triangle. -The three altitudes of an obtuse triangle are concurrent at a point that lies in the exterior of that triangle.

(True/False)
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