honors geometry ruggiero quarterly #2

hate his class

cpcfc

cpcfc

corresponding parts of congruent figures are congruent

cpctc

corresponding parts of congruent triangles are congruent

linear pair

Two adjacent angles that form a straight line (180 degrees)

vertical angle

opposite angles formed by the intersection of two lines

vertical angle theorem

Vertical angles are congruent

corresponding angles

lie on the same side of the transversal and in corresponding positions

same-side interior angles

interior angles that lie on the same side of the transversal

alternate interior angles

Interior angles that lie on opposite sides of the transversal

alternate exterior angles

two exterior angles on opposite sides of a transversal

same-side exterior angles

two exterior angles on the same side of the transversal

Same-Side Interior Angles Theorem

if 2 parallel lines are cut by a transversal, pairs of same-side interior angles are supplementary

alternate-interior angles theorem

if 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Corresponding Angles Theorem

If a transversal intersects two parallel lines, then corresponding angles are congruent.

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

ASA Theorem

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

Congruent Supplements Theorem

If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.

SAS Theorem

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.

regular polygon

all sides are congruent and all angles are congruent

SSS Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

HL Theorem (hypotenuse-leg)

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180 degrees

Polygon Angle Sum Theorem

The sum of the interior angle measures of a convex polygon with n sides is (n-2)180

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.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Converse of the Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Equilateral Triangle Theorem

If a triangle is equilateral, then it is equiangular

Converse of the Equilateral Triangle Theorem

If a triangle is equiangular, then it is equilateral.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

circumscribed

circle that has all vertices of a polygon

circumcircle

a circle (idk)

circumcenter

center of circle

concurrent

3+ lines when they intersect at the same point

circumcenter theorem

the perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle

Where is the circumcenter in an acute triangle?

inside

Where is the circumcenter in an right triangle?

on hypotenuse

Where is the circumcenter in an obtuse triangle?

outside

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle

inscribed

each side of the polygon is tangent to the circle

incenter

the point of concurrency of the angle bisectors

Incenter Theorem

The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.

median

a segment from a vertex to the midpoint of the opposite side

centroid

The point of concurrency of the medians of a triangle

centroid theorem

The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side

altitude

a perpendicular segment from a vertex to the line containing the opposite side

orthocenter

The point of concurrency of the altitudes of a triangle