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Geometry and Trig Chapter 3 vocab

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Congruent figures
two or more figures with the same shape & size
Triangle
a 3 sided polygon
6 parts of a triangle
3 angles and 3 sides
congruent polygons
all pairs of corresponding parts (sides/angles) are congruent
congruent triangles
all 6 pairs of parts of a triangle are congruent
reflexive property
an angle or segment is congruent to itself
included angle
angle formed by 2 sides of a triangle
included sides
the common side between 2 angles of a triangle
Side Side Side Postulate
if 3 sides of a triangle are congruent to the corresponding 3 sides of a 2nd triangle then the triangles are congruent
Side Angle Side Postulate
if 2 sides and their included angle of a triangle are congruent to the corresponding 2 sides and their included angle of a 2nd triangle then the triangles are congruent
Angle Side Angle Postulate
if 2 angels and their included side of a triangle are congruent to the corresponding 2 angles and their included angle of a 2nd triangle then the triangles are congruent
CPCTC
Corresponding Parts Congruent Triangles Congruent
Circle
an infinite collection of points that are the same distance from a central point (known as the center)
Center
The point at the same distance from all the points of a circle
radius
a segment with an endpoint on a circle and an endpoint that is the center of the circle
Circumference
C = 2πr
Area
A = πr^2
types of triangles
Scalene, Isosceles, equilateral, and equiangular
Scalene triangle
A triangle with no congruent sides
Isosceles triangle
A triangle with at least 2 congruent sides
Equilateral triangle
A triangle with all 3 sides congruent
Equiangular triangle
a triangle with all 3 angles congruent
legs of isosceles triangle
Congruent sides of isosceles triangles
base of isosceles triangle
non-congruent side of isosceles triangle
Vertex angles
angle of an isosceles triangle when sides are the legs of the triangle
Base angles
angles of an isosceles triangle who have the base as one of their sides
Angle classification
acute, right, and obtuse
acute
A triangle which has 3 acute angles
right
a triangle with exactly one right angle
obtuse
a triangle with exactly 1 obtuse angle
triangle sum theorem
the measure of the 3 interior angles of a triangle sum to 180 degrees
No choice theorem
if 2 angles form one triangle congruent to the 2 angles in the second triangle the pair of angles are congruent
Angle Angle Side Postulate
if two angles and one side form a triangle congruent to the two angels and side in the second triangle the triangles are congruent
Hypotenuse
side opposite the right angle in a right triangle
legs of a right triangle
two side in a right triangle that form the right angle
median
a segment drawn from the vortex of a triangle to the midpoint of the opposite side
altitude
a segment drawn from the vortex of a triangle perpendicular to the opposite side (extend if necessary)
Angle side
- if two sides in a triangle are congruent then the angles opposite those sides are also congruent - if two angles in a triangle are congruent then the sides opposite them are congrurent
Angle side for Scalene triangles
- if two sides of a triangle are not congruent, then the angles opposite then are also not congruent and the larger angle is opposite the larger side - if two angles of a triangle are not congruent, then the sides opposite of them are also not congruent and the longer side is opposite if the larger angle
Hypotenuse leg Postulate
if the hypotenuse and a leg of a right triangle are congruent to the corresponding hypotenuse and leg of a 2nd right triangle then the triangles are congruent
auxiliary lines postulate
2 points that make a segment