ASA Theorem

If 2 angles & the included side of 1 angle are equal to the corresponding angles and side of another triangle, then the angles are congruent.

AAS Theorem

If two angles and a non-included side of 1 triangle are equal to corresponding angles and side of another triangle, then the triangles are equal.

ASS

ASS IZ NOT GOOD

SAS Postulate

If 2 sides & the included angle of 1 triangle are equal to the corresponding sides & angles of another triangle, then the triangles are congruent.

SSS Postulate

If 3 sides of 1 triangle are equal to the corresponding sides of another triangle, then the triangles are congruent.

angle bisector

a ray that begins in the vertex of an angle & divides the angle into 2 equal parts

segment bisector

a ray, line, or segment that divides a segment into two equal parts

perpendicular bisector

a line, ray, / seg tht bisects the seg & is perp to it

Hypotenuse-Leg Theorem

2 right triangles are equal if the hypot & leg of 1 triangle are equal to the hyp & leg of the other triangle.

isosceles triangle

a triangle w/ 2 sides = in measure

equilateral triangle

a triangle in which all the sides are equal in measure

equiangular triangle

a triangle in which all the angles are equal in measure

Isosceles Triangle Theorem

If 2 sides of a triangle of a triangle are = in measure, then the angles opp. those sides r = in msr.

Converse of Isosceles Triangle Th

If 2 angles of a triangle are equal in msr, then the sides opp those angles r = in msr

Equilateral Triangle Theorem

If a triangle is equilateral, then it's also equiangular.

Converse of Equil Triangle Th

If a triangle is equiangular, then it's equilateral.

Perpendicular Bisector Th

If a point is the same distance from both end points of a segment, then it lies on the perpendicular bisector of the segment.

Similar Right Triangle Th

If the altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed are similar to each other & the original triangle.

geometric mean

If a, b, and x are positive numbers, and a/x = x/b, then x is the geometric mean b/w a and b. The gm is ALWAYS the positive root.

Geometric Mean Th

If the alt is drawn to the hypotenuse of a right triangle, then the measure of the altitude is the geometric mean b/w the measures of the parts of the hypotenuse.

If 2 angles & the included side of 1 angle are equal to the corresponding angles and side of another triangle, then the angles are congruent.

ASA Theorem

If two angles and a non-included side of 1 triangle are equal to corresponding angles and side of another triangle, then the triangles are equal.

AAS Theorem

If 2 sides & the included angle of 1 triangle are equal to the corresponding sides & angles of another triangle, then the triangles are congruent.

SAS Postulate

If 3 sides of 1 triangle are equal to the corresponding sides of another triangle, then the triangles are congruent.

SSS Postulate

2 right triangles are equal if the hypot & leg of 1 triangle are equal to the hyp & leg of the other triangle.

Hypotenuse-Leg Theorem

If 2 sides of a triangle of a triangle are = in measure, then the angles opp. those sides r = in msr.

Isosceles Triangle Theorem

If 2 angles of a triangle are equal in msr, then the sides opp those angles r = in msr

Converse of Isosceles Triangle Th

If a triangle is equilateral, then it's also equiangular.

Equilateral Triangle Theorem

If a triangle is equiangular, then it's equilateral.

Converse of Equil Triangle Th

If a point is the same distance from both end points of a segment, then it lies on the perpendicular bisector of the segment.

Perpendicular Bisector Th