Polygons and Triangles Vocab

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