Triangles
If we know the sine, cosine, or tangent ratio for an angle, we can use an ______________
to find the measure of the angle.
inverse (sin-1, cos-1, or tan-1)
In a plane, if two lines are perpendicular to the same line, then they are __________ to each other.
parallel
A segment whose endpoints are a vertex and the midpoint of the opposite side.
Median
A quadrilateral whose:
a) opposite sides are congruent
b) opposite angles congruent
c) consecutive angles are supplementary
d) diagonals bisect each other
parallelogram
Prism:
A) Surface Area =
b) Volume =
1) The surface area SA of a right prism is
SA = 2B + Ph
where B is the area of a base, P is the perimeter of a base, and h is the height of the prism.
2) V = Bh
where B is the area of the base and h is the height of the prism.
The measure of each exterior angle of a triangle equals the sum of the measures of its two _____ _____ angles.
two nonadjacent interior angles.
Which Theorem states :
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.
alternate interior angles theorem
Medians of a triangle are concurrent at a point called
centroid
A parallelogram is ________
a) four congruent sides
b) diagonals are perpendicular
c) diagonals bisect a pair of opposite angles
rhombus
Cylinder:
1) Surface Area =
2) Volume
1) SA = 2B + 2(pi)rh
2) V = Bh or (pi)r2h
where B is the area of the base (so we know that B = πr2) and h is the height of the cylinder.
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent by ________ postulate
Angle - Side - Angle (ASA)
Same-Side interior angles when added measure
180 degrees
The lines that contain the altitudes of a triangle are concurrent at the __________ of the triangle
orthocenter
A __________ is a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.
kite
Pyramid:
1) Surface Area
2) Volume
1) Surface Area = B + 1/2 P l
where B is the area of the base, P is the perimeter of the base, and l is the slant height.
2) V = 1/3 Bh
where B is the area of the base and h is the height of the pyramid
In a 45°-45°-90° triangle, both legs are
congruent and the length of the hypotenuse is
√2 times the length of a leg.
A line that intersects two or more coplanar lines at different points
Transversal
a segment connecting the midpoints of two sides of the triangle
midsegment of a triangle
The parallel sides of a this quadrilateral are called bases. The nonparallel sides are called legs.
trapezoid
Cone:
1) Surface Area
2) Volume
1) SA = B + (pi) r l
where B is the area of the circular base ((pi)r2), r is the radius of the base, and l is the slant height
2) V = 1/3 Bh
where B is the area of the circle base (we know that
B = (pi)r2)
1)In a 30°-60°-90° triangle, the length of the
hypotenuse is _________
2) The length of the longer leg is ____________
1) twice the length of the shorter leg
2) √3 times the length of the shorter leg.
Nonadjacent exterior angles that lie on opposite sides of the transversal
alternate exterior angles
What is the distance between the vertex of a triangle and the centroid?
The centroid is two-thirds the distance from each vertex to the midpoint of the opposite side
Length of the midsegment of a trapezoid
half the sum of the lengths of the bases
Sphere:
1) Surface Area
2) Volume
1) SA = 4 (pi) r2
where r is the radius of the sphere.
2) V = 4/3 (pi) r3
where r is the radius of the sphere.