Studied by 3 people
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Polygon
A closed plane figure formed by 3 or more line segments
Consecutive vertices
2 vertices that are endpoints of the same side
Diagonal
A segment that joins 2 consecutive vertices
Interior angles
Original angles
Exterior angles
Angles that form linear pairs with the interior angles
Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex polygon, one angle at each vertex is 180 degrees
Corollary to the Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a quadrilateral is 360 degrees
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180 degrees
Corollary to Triangle Sum Theorem
The acute angles of a right triangle are complementary (add to 90)
Polygon Exterior Angles Theorem
The sun of the measures of the exterior angles of a convex polygon, one angle at each vertex is 360
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles
Equilateral polygon
All sides are congruent
Equiangular Polygon
All angles are congruent
Regular polygon
Both equilateral and equiangular
Scalene triangles
No congruent sides
Isosceles triangle
At least 2 congruent sides
Base Angles Theorem
If 2 sides of a triangle are congruent then the angles opposite to them are congruent (converse works too)
Corollary to the Base Angles Theorem and its Converse
If a triangle is equilateral, then it is also equiangular
Median
A segment from a vertex to the midpoint of the opposite side
Centroid
A point where three or more lines, rays or segments meet and will fall inside of the triangle
Altitude
The perpendicular line segment from a vertex to the opposite side or to the line that contains the opposite
Orthocenter
The point of concurrency of the lines containing the altitudes of a triangle
Midsegment of a triangle
Segment that connects the midpoints of two sides of the triangle
Triangle midsegment theorem
The segment connecting the two sides of a triangle is parallel to the 3rd side and half as long as that side
Triangle Longer Side Theorem
If one side of triangle is longer than another— the angle opposite of the longer side is larger than the angle opposite of the shorter side
Triangle Larger Angle Theorem
If an angle of a triangle is larger than another angle, then the side opposite that larger angle is longer than the opposite side of the smaller angle
Triangle Inequality theorem
The sum of the lengths of the 2 sides of a triangle is greater than the length of the third side
Hinge Theorem and converse
If two sides of one triangle are congruent to two sides of another triangle and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second
