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71 Cards in this Set

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  • Back
The sum of the measures of the angles in every triangle is...
180 degrees
If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle is...
equal in measure to the third angle in the other triangle
If a triangle is isosceles, then the base angles are...
congruent
If a triangle has two congruent angles...
then it is an isosceles triangle
The sum of the lengths of any two sides of a triangle is...
greater than the length of the third side
In a triangle, if one side is longer than another side, then the angle opposite the longer side is...
larger than the angle opposite the smaller side
The measure of an exterior angle of a triangle is equal to...
the sum of the measures of the remote interior angles
If three sides of one triangle are congruent to the three sides of another triangle, then...
the triangles are congruent (SSS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then...
the triangles are congruent (SAS)
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then...
the triangles are congruent (ASA)
If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then..
the triangles are congruent (SAA)
In an isosceles triangle, the bisector of the vertex is also...
the altitude and the median to the base
Every equilateral triangle is...
equiangular
Every equiangular triangles is...
equilateral
The sum of the measures of the four angles in any quadrilateral is...
360 degrees
The sum of the measures of the n interior angles of an n-gon is...
180○(n-2)
For any polygon, the sum of the measures of a set of exterior angles is...
360○
You can find the measure of each interior angle of an equiangular n-gon by using either formula:
180○ - 360○/n
OR
180○(n-2) / n
The nonvertex angles of a kite are...
congruent
The diagnoals of a kite are...
perpendicular
The diagonal connecting the vertex angles of a kite is...
the perpendicular bisector of the other angle.
The vertex angles of a kite are bisected by...
a diagonal
The consecutive angles between the bases of a trapezoid are...
supplementary
The base angles of an isosceles trapezoid are...
congruent
The diagonals of an isosceles trapezoid are...
congruent
The three midsegments of a triangle divide it into...
four congruent triangles
A midsegment of a triangle is...
parallel to the third side and half the length of the third side
The midsegment of a trapezoid is...
parallel to the bases and is equal in length to the average of the lenths of the bases
The opposite angles of a parallelogram are...
congruent
The consecutive angles of a parallelogram are...
supplementary
The opposite sides of a parallelogram are
congruent
The diagonals of a parallelogram...
bisect each other
If two chords are congruent then they determine...
two central angles that are congruent
The measure of an arc is defined as...
the measure of its central angle
If two chords in a circle are congruent then...
their intercepted arcs are congruent
The perpendicular from the center of a circle to a chord is...
the bisector of the chord
Two congruent chords in a circle are equidistant from...
the center of the circle
The perpendicular bisector of a chord goes through...
the center of the circle
A tangent to a circle is perpendicular to...
a radius drawn to the point of tangency
Tangent segments to a circle from a point outside the circle are...
congruent
The measure of an inscribed angle in a circle is...
one half the measure of the central angle
Inscribed angles that intercept the arc are...
congruent
Angles inscribed in a semi-circle are...
right angles
(note: the inscribed angle intercepts and arc that is 180 degrees, so the angle must measure 90 degrees)
The opposite angles of a cyclic quadrilateral are...
supplementary
What is a cyclic quadrilateral?
a quadrilateral inscribed in a circle
What is a secant?
a line that intercepts a circle in two points, contains a chord of the circle and passes through the circle (not a tangent)
What is a scalene triangle?
has no congruent sides
What is a trapezoid?
A quadrilateral with exactly one pair of parallel lines
What is a kite?
a quadrilateral with two distinct pairs of consecutive congruent sides
What is a parallelogram?
quadrilateral with two pairs of parallel lines
What is a rhombus?
an equilateral parallelogram
What is a rectangle?
a prallelogram with 4 congruent angles
What is a square?
an equilateral rectangle, an equilateral parallelogram, a regular quadrilateral
What is a sector of a circle?
the region between 2 radii and the included arc.
What is a segment of a circle?
the region between the chord of a circle and the included arc
What is an annulus?
region between two concentric circles
How do find the area of a sector?
a=arc
a/360(πr^2)
How do you find the area of a segment?
b=base
a=altitude
r=radius
a/360(r^2) - 1/2(bh)
How do find the area of an annulus?
πR^2 - πr^2
On a circle, parallel lines intercept...
congruent arcs
How do you find the length of an arc?
the circumference times the measure of the central angle divided by 360 degrees
How do you find the area of a rectangle?
b=length of base
h=height of rectangle

A=bh
How do you find the area of a parallelogram?
b=length of base
h=height of parallelogram

A=bh
How do you find the area of a triangle?
b=length of base
h=heigh of triangle

A=1/2(b)(h)
How do you find the area of a trapezoid?
b1 and b2=lengths of bases
h=height of trapezoid

A=1/2(b1+b2)h
How do you find the area of a kite?
d1 and d2=lengths of diagonals

A=1/2(d1)(d2)
How do you find the area of a circle?
r=radius

A=πr^2
What is a central angle?
has its vertex at the center of the circle
What is an inscribed angle?
angle with vertex on the circle, sides are chords
How do you find the surface area of a pyramid?
l=slant height
n=number of faces

A=1/2(n)(b)(l+a)
How do you find the surface area of a cone?
A=πr(r+l)