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

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  -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ? -To determine the measure of   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ? , which expression should be calculated.   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ? (m   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ?   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ? m   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ? ) or   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ? (m   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ?   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ? m   -To determine the measure of   , which expression should be calculated.   (m     m   ) or   (m     m   ) ? ) ?

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  -In the figure,   . What reason allows you to conclude that   ? -In the figure,   -In the figure,   . What reason allows you to conclude that   ? . What reason allows you to conclude that   -In the figure,   . What reason allows you to conclude that   ? ?

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For a rectangle with base length of 1 foot and height 6 inches, the area is 6 For a rectangle with base length of 1 foot and height 6 inches, the area is 6   . .

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  -To construct the altitude from vertex A to side   of the obtuse triangle   , one begins by constructing the midpoint of   . -To construct the altitude from vertex A to side   -To construct the altitude from vertex A to side   of the obtuse triangle   , one begins by constructing the midpoint of   . of the obtuse triangle   -To construct the altitude from vertex A to side   of the obtuse triangle   , one begins by constructing the midpoint of   . , one begins by constructing the midpoint of   -To construct the altitude from vertex A to side   of the obtuse triangle   , one begins by constructing the midpoint of   . .

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If the measures of the angles of a quadrilateral ABCD are in the extended ratio If the measures of the angles of a quadrilateral ABCD are in the extended ratio   , what type of quadrilateral is ABCD? , what type of quadrilateral is ABCD?

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  -For the right triangular prism shown, the sides of the base measure 6 cm, 8 cm, and 10 cm. If the height of the prism is 12 cm, find the total area of the prism. -For the right triangular prism shown, the sides of the base measure 6 cm, 8 cm, and 10 cm. If the height of the prism is 12 cm, find the total area of the prism.

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  -In   , AB = 6 cm, AD = 10 cm, and m   = 65°. To the nearest tenth of centimeter, find the length of altitude   from B to side   . -In   -In   , AB = 6 cm, AD = 10 cm, and m   = 65°. To the nearest tenth of centimeter, find the length of altitude   from B to side   . , AB = 6 cm, AD = 10 cm, and m   -In   , AB = 6 cm, AD = 10 cm, and m   = 65°. To the nearest tenth of centimeter, find the length of altitude   from B to side   . = 65°. To the nearest tenth of centimeter, find the length of altitude   -In   , AB = 6 cm, AD = 10 cm, and m   = 65°. To the nearest tenth of centimeter, find the length of altitude   from B to side   . from B to side   -In   , AB = 6 cm, AD = 10 cm, and m   = 65°. To the nearest tenth of centimeter, find the length of altitude   from B to side   . .

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  -In   , m   = 84° and m   = 42°. The bisectors of   and   meet at the point V in the interior of   . What is the measure of   ? -In   -In   , m   = 84° and m   = 42°. The bisectors of   and   meet at the point V in the interior of   . What is the measure of   ? , m   -In   , m   = 84° and m   = 42°. The bisectors of   and   meet at the point V in the interior of   . What is the measure of   ? = 84° and m   -In   , m   = 84° and m   = 42°. The bisectors of   and   meet at the point V in the interior of   . What is the measure of   ? = 42°. The bisectors of   -In   , m   = 84° and m   = 42°. The bisectors of   and   meet at the point V in the interior of   . What is the measure of   ? and   -In   , m   = 84° and m   = 42°. The bisectors of   and   meet at the point V in the interior of   . What is the measure of   ? meet at the point V in the interior of   -In   , m   = 84° and m   = 42°. The bisectors of   and   meet at the point V in the interior of   . What is the measure of   ? . What is the measure of   -In   , m   = 84° and m   = 42°. The bisectors of   and   meet at the point V in the interior of   . What is the measure of   ? ?

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  -The area of a circle is 27.5   . To the nearest tenth of a square inch, find the area of the square that is circumscribed about this circle. -The area of a circle is 27.5   -The area of a circle is 27.5   . To the nearest tenth of a square inch, find the area of the square that is circumscribed about this circle. . To the nearest tenth of a square inch, find the area of the square that is circumscribed about this circle.

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Find the slope of a line that is perpendicular to the line through the points (a,b) and ( Find the slope of a line that is perpendicular to the line through the points (a,b) and (   ). ).

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  -In the circle, m   = 102° and m   = 76°. Where M is the midpoint of   , find m   . -In the circle, m   -In the circle, m   = 102° and m   = 76°. Where M is the midpoint of   , find m   . = 102° and m   -In the circle, m   = 102° and m   = 76°. Where M is the midpoint of   , find m   . = 76°. Where M is the midpoint of   -In the circle, m   = 102° and m   = 76°. Where M is the midpoint of   , find m   . , find m   -In the circle, m   = 102° and m   = 76°. Where M is the midpoint of   , find m   . .

(Short Answer)
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The exact value for both sin 45° and cos 45° is The exact value for both sin 45° and cos 45° is   . .

(True/False)
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From an external point E, tangents From an external point E, tangents   and   are drawn to   . If m   = 78°, find the measure of minor arc   . and From an external point E, tangents   and   are drawn to   . If m   = 78°, find the measure of minor arc   . are drawn to From an external point E, tangents   and   are drawn to   . If m   = 78°, find the measure of minor arc   . . If m From an external point E, tangents   and   are drawn to   . If m   = 78°, find the measure of minor arc   . = 78°, find the measure of minor arc From an external point E, tangents   and   are drawn to   . If m   = 78°, find the measure of minor arc   . .

(Short Answer)
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  -In the figure, chords   and   intersect at point X. If RX = 8, TX = 12, and XS = 9, find XV. -In the figure, chords   -In the figure, chords   and   intersect at point X. If RX = 8, TX = 12, and XS = 9, find XV. and   -In the figure, chords   and   intersect at point X. If RX = 8, TX = 12, and XS = 9, find XV. intersect at point X. If RX = 8, TX = 12, and XS = 9, find XV.

(Multiple Choice)
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In a circle in which m In a circle in which m     m   , it follows that   . In a circle in which m     m   , it follows that   . m In a circle in which m     m   , it follows that   . , it follows that In a circle in which m     m   , it follows that   . .

(True/False)
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  -  is circumscribed about   in such a way that   . Which angle of   has the greatest measure? -  -  is circumscribed about   in such a way that   . Which angle of   has the greatest measure? is circumscribed about   -  is circumscribed about   in such a way that   . Which angle of   has the greatest measure? in such a way that   -  is circumscribed about   in such a way that   . Which angle of   has the greatest measure? . Which angle of   -  is circumscribed about   in such a way that   . Which angle of   has the greatest measure? has the greatest measure?

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  can also be called   . can also be called   can also be called   . .

(True/False)
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A line through the center of a circle perpendicular to a chord (not a diameter) bisects the chord.

(True/False)
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  -The length of radius of the circle shown is 10 inches. If CD = 12 inches and AB = 16 inches, how much closer to the center is chord   than   ? -The length of radius of the circle shown is 10 inches. If CD = 12 inches and AB = 16 inches, how much closer to the center is chord   -The length of radius of the circle shown is 10 inches. If CD = 12 inches and AB = 16 inches, how much closer to the center is chord   than   ? than   -The length of radius of the circle shown is 10 inches. If CD = 12 inches and AB = 16 inches, how much closer to the center is chord   than   ? ?

(Multiple Choice)
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A regular icosahedron has its faces numbered 1, 2, 3, . . . , 20 and is used as a die. What is the probability that a roll produces a multiple of 5?

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