Postulates
A reflection is a rigid motion.
What is a Reflection Postulate?
If a triangle is equiangular, then it is equilateral.
What Is Corollary to the Converse of the Base Angles Theorem?
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent
What is Side-Angle-Side Congruence Theorem?
The acute angles of a right triangle are complementary.
What is Corollary to the Triangle Sum Theorem?
In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel.
What is Slopes of Parallel Lines?
A translation is a rigid motion.
What is a Translation Postulate?
if two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.
What is Consecutive Interior Angles Converse Theorem?
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
What is Side-Side-Side (SSS) Congruence Theorem?
The sum of the measures of the interior angles of a triangle is 180°.
What is Triangle Sum Theorem?
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is −1. Horizontal lines are perpendicular to vertical lines.
What is Slopes of Perpendicular Lines?
A rotation is a rigid motion.
What is a Rotation Postulate?
if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
What is the Converse Corresponding Angles Theorem?
if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
What Is Hypotenuse-Leg (HL) Congruence Theorem?
If two angles of one triangle are congruent to two angles of another
What is Third Angles Theorem?
If two lines are parallel to the same line, then they are parallel to each other.
What is Transitive Property of Parallel Lines?
What is a Perpendicular Postulate?if there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
What is a Perpendicular Postulate?
If two angles of a triangle are congruent, then the sides opposite them are congruent.
What is a Converse of the Base Angles Theorem?
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
What is Angle-Side-Angle (ASA) Congruence Theorem?
If two sides of a triangle are congruent, then the angles opposite them are congruent.
What is Base Angles Theorem?
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
What is Linear Pair Perpendicular Theorem?
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
What is a Parallel Postulate?
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
What is Alternate Interior Angles Converse Theorem?
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
What is Angle-Angle-Side (AAS) Congruence Theorem?
congruence is reflexive, symmetric, and transitive. Refl exive For any triangle △ABC, △ABC ≅ △ABC. Symmetric If △99uup ABC ≅ △DEF, then △DEF ≅ △ABC. Transitive If △A
What Is Properties of Triangle Congruence Triangle?
If a triangle is equilateral, then it is equiangular.
What is Corollary to the Base Angles Theorem