Kehrt's Honors Geometry Final
If two sides of a triangle measure 14 cm and 10 cm, and the angle between the sides measures 30º, then the area of the triangle is ________.
???
If a circle has area 32π ft^2, then a 135º sector of the circle has area ______.
?????
The density of a substance is calculated by dividing its ______ by its ________.
mass; volume
The only polygons that can be used to form a regular tessellation are equilateral triangles, regular hexagons, and _______.
octagons
If a line cuts two sides of a triangle proportionally, then it is _______ to the third side.
parallel
Each point on the _____________ of a segment is equidistant from the endpoints of the segment.
perpendicular bisector
The line of reflection is the ____________ of every segment joining a point in the original figure with its image.
perpendicular bisector
The three undefined terms in geometry are:
point, line, and plane
A circle with equation x^2 + (y+4)^2 = 9 has center ______ and radius ______.
(0, -4); 3 !!!
The ordered pair rule (x, y) → _______ represents a reflection over the x-axis.
(x, -y)
Find the missing term of each sequence: 10, 9, 7, 4, 0, -5, ___
-11
If a 90º arc of a circle has length 5π inches, then the radius of the circle is ______.
10 in.; ?????
If one of the base angles of an isosceles triangle has measure 40º, then the vertex angle has measure _____º.
100º; 40+40=80, 180-80=100
In a regular pentagon, each interior angle has measure _____º.
108º; 180(n-2)/n
If ∠1 and ∠2 form a linear pair and m∠1 = 64º, then m∠2 is ____º.
116
The surface area of a cube with edge length 5 in. is ______.
150 in^2; 6a^2 = 6(5)^2 = 150
If cosB = 4/5, and sinB = 3/5, then tanB = __________.
3/4
Find the missing term of each sequence: 1, 4, 9, 16, 25, ___
36
In a regular n-gon, each exterior angle has measure _____.
360/n
A triangle has an area of 12cm^2. If the length of one side of the triangle is 6 cm, then the length of the altitude (height) to that side must be ______.
4 cm; 12= 1/2(6)h, 12=3h, h=4
How many diagonals does a polygon with 32 sides have?
464; n(n-3)/2
If the surface areas of two similar cylinders are in the ratio 64/81, then the volumes are in the ratio ________.
6^3/9^3?
If the midsegment of a trapezoid has length 6 cm, and one of the bases has length 4 cm, then the other base has length _____.
8 cm; x+4/2=6/1, x+4=12, x=8
A chunk of copper is dropped into a container, causing the water level to rise 2 cm. The container is a rectangular prism with base 6 cm by 5 cm. What is the density of copper?
8.97 gm/cm^3; 538.2/30=17.94, 17.94/2= 8.97
If a circle has circumference 18π cm, then its area is ______.
81π; 2πr=18π, divide that by π, 2r=18, r=9, a=π9^2, A=81π
A square with a diagonal length of 14 cm has area ______.
?
If the length of the longer leg of a 30º 60º 90º triangle is x, then the length of the shorter leg is ______ and the length of the hypotenuse is _______.
?;?
If the rule (x, y) → (3x, 3y) is applied to a triangle with area 6 cm^2, then the area of the image triangle is ________.
???
In △ ABC, if m∠A = 50º, m∠B = 72º, and m∠C = 58º, then _____ is the longest side.
AC
True or False: A diagonal of a square divides it into two equilateral triangles.
False
True or False: A trapezoid has exactly one pair of congruent sides.
False
True or False: Given two side lengths and one angle measure of a triangle, you can always use the Law of Sines to find the measure of another angle.
False
True or False: If the opposite angles of a parallelogram are supplementary, then the parallelogram is a rectangle.
False
True or False: If ∠A is an acute angle in a right triangle, then cos A= length of leg opposite ∠A/ length of hypotenuse
False
True or False: In a linear pair of angles, one of the angles must be obtuse.
False
True or False: Only one plane can pass through one line and a point that is not on the line.
False
True or False: The diagonals of a kite bisect each other.
False
True or False: The tangent to a circle is a special type of chord.
False
True or False: The sum of the measures of the interior angles of an octagon is 1440º.
False; (n-2)180= 1080º
True or False: The semicircle has an arc measure of 360º.
False; 180
True or False: The formula for the surface area of a sphere with radius r is S= 4/3πr^2.
False; 4πr^2
True or False: It is possible to create a triangle with side lengths 12 cm, 7 cm, and 5 cm.
False; 7+5= 12-- the sum of the two smaller sides cannot be equal to or smaller than the largest side
True or False: If two sides and a non-included angle of one triangle are congruent to two sides and a non-included angle of another triangle, then the triangles are congruent.
False; A-S-S doesn't work
True or False: ∠ABC has vertex C.
False; B
True or False: The incenter of a triangle is the intersection of the perpendicular bisectors of its sides.
False; circumcenter
True or False: When you construct a figure, you use only a compass and a protractor.
False; compass and straightedge
True or False: The process of observing data, recognizing patterns, and making generalizations about those patterns is known as deductive reasoning.
False; inductive reasoning
True or False: In a parallelogram, the opposite angles are complimentary.
False; supplementary
True or False: The opposite angles of a quadrilateral inscribed in a circle are congruent.
False; supplementary
True or False: If the edge lengths of two similar prisms are in the ratio p/q, then the (surface areas) of the prisms are in the ratio p^3/q^3.
False; volumes
True or False: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
False?
Is the triangle with vertices L(4, -3), M(2, 1), N(-2, -1) scalene, isosceles, or equilateral?
Isosceles; LM=MN=√20, while LN=√40
How do you construct parallel lines?
The rhombus method
True or False: A cube is an octahedron.
True
True or False: A scalene triangle has no sides of the same length.
True
True or False: A square is both a rhombus and a rectangle.
True
True or False: Any two squares are similar.
True
True or False: If a cone and a cylinder have the same radius and the same height, then the volume of the cone is 1/3 the volume of the cylinder.
True
True or False: If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
True
True or False: If two lines are cut by a transversal to form a pair of congruent corresponding angles, then the lines are parallel.
True
True or False: In an equilateral triangle, the bisector of an angle is also the altitude to the side opposite of the angle.
True
True or False: Parallel lines intercept congruent arcs on a circle.
True
True or False: The center of a circle lies on the perpendicular bisector of every chord of the circle.
True
True or False: The centroid of a triangle is the center of gravity for the triangle.
True
True or False: The diagonals of an isosceles trapezoid are congruent.
True
True or False: The ratio circumference/diameter is the same for every circle.
True
True or False: The tangent to a circle is perpendicular to the radius drawn to the point of tangency.
True
True or False: Given two angles and an included side, you can construct exactly one triangle.
True; A-S-A
A(n) _______ triangle has angle measures that are all less than 90º.
acute
Two polygons are similar if and only if corresponding angles are _______ and the corresponding sides are ________.
congruent; proportional?
A(n) _______ is a chord that passes through the center of a circle.
diameter
The _______ of a triangle is the center of the circle inscribed in the triangle
incenter
In a right triangle, if m and n are the lengths of the legs and p is the length of the hypotenuse, then _________.
m^2+n^2 = p^2
Angles inscribed in a semicircle are _____ angles.
right
The two diagonals of a ______ are perpendicular bisectors of one another, are congruent, and bisect the angles.
square
A _________ is a transformation that slides a figure along a straight-line path, moving each point the same distance in the same direction.
translation
A composition of two reflections over two parallel lines is equivalent to a single _______.
translation
If a cylinder has height 4 cm and base diameter x cm, then its volume is ________.
π(1/2x)^2(4); v= πr^2H
The distance between points (-3, 7) and (-12, 3) is ________.
√97 units; d= √(x2-x1)^2+(y2-y1)^2, d= √(-12+3)^2+(3-7)^2, d= √81+16, d= √97
A translation of ⟨6, -4⟩ followed by a translation of ⟨-3, -5⟩ is equivalent to a translation of ______.
⟨3, -9⟩