final Flashcards
what is a triangle?
a closed figure in a plane consisting of 3 segments called sides
how are triangles named?
using the capital letters assigned to its vertices in a clockwise or counterclockwise direction
what are the properties of a scalene triangle?
no sides are congruent and no angles are congruent
what are the properties of a isosceles triangle?
at least two sides are congruent and two angles called the base angles are congruent
what are the properties of an equilateral triangle?
all three sides are congruent and all three angles are congruent
what are the properties of a right triangle?(op)
-exactly one angle is a right angle
-the acute angles are complementary
-the side opposite the right angle called the hypotenuse is the longest side
what are the properties of an acute triangle?(op)
- all three angles are acute
what are the properties of an obtuse triangle?(op)
exactly one angle is an obtuse angle
what is the triangle-angle sum theorem
m<A+m<B+m<C=180°
what is the exterior angle theorem?
m<1=m<A+m<B
what is the pythagorean theorem?
c^2=a^2+b^2
what is the hypotenuse and what is its notation
the side opposite the right angle in a right angled triangle
often denoted as ‘c’
what are the legs and what are their notation
the two shorter sides that form the right angle
often denoted as ‘a’ an ‘b’
what is the converse of the pythagorean theorem?
if the sum of the measure of the two legs of a triangle equals the square of the measure of the longest side then the triangle is a right triangle
if c^2<a^2+b^2 then the triangle is
an acute triangle
what is a radius
a line segment from the center to a point on the circle
if c^2=a^2+b^2 then the triangle is
a right triangle
if c^2>a^2+b^2 the the triangle is
an obtuse triangle
what is a circle
a set of all point in a plane that are the same distance from a given point called the center of the circle
what is a chord
a segment with endpoints on the circle
what is a diameter
a chord that passes through the center of the circle
what is the circumference
the distance around the circle
what is the formula for diameter
d=2xr
what is the formula for the radius
r=d/2
what is the formula for circumference
c=2πr
what is a central angle of a circle
an angle with a vertex at the center of the circle and sides that are radii
what is the formula to get the sum of the central angles
m<1+m<2+m<3=360°
a minor arc has a measure of
less than 180°
what is an arc
part of a circle that is defined by two endpoints
a major arc has a measure of
more than 180°
a semicircle has a measure of
exactly 180°
what is the arc length
the distance between the endpoints of an arc measured along the arc in linear units.
what are congruent arcs
arcs that have the same measure
what are adjacent arcs
arcs that have exactly one point in common
what is the formula to find the length
l= x/360 x 2πr
what is a radian
a unit of angular measurement equal to 180°/π
degree –> radians
π radians/ 180°
radians –> degree
180°/ π radians
what is a quadrilateral
four sided figure
what is the area
the space inside the shape
what is a rectangle
a quadrilateral with both pairs of opposite sides parallel and equal and four right angles
what is a square
a quadrilateral with 4 equal sides and 4 right angles the opposite sides in a square are both parallel and equal in length
how to find the area of a square
A= a^2
how to find the area of a rectangle
a=lxw
how to find the area of a parallelogram
a=bxh
what is the base of a parallelogram
any side of the parallelogram
what is a parallelogram
quadrilateral with both pairs of opposite sides parallel and equal(2 pairs of parallel sides)
what is the height of a parallelogram
the length of the altitude(perpendicular) of the parallelogram
what is a trapezoid
a quadrilateral with exactly one pair of parallel sides(1 pair of parallel sides)
how to find the area of a trapezoid
A= 1/2 h (b1+b2)
what is a kite
a quadrilateral with exactly 2 pairs of consecutive congruent sides(2 consecutive equal sides)
what is a rhombus
a parallelogram with all four sides congruent(2 pairs of parallel sides, all sides are congruent)
what is the area of a kite/rhombus
a=1/2(d1d2)
