Postulates and Proofs Flashcards
What does the Angle Addition Postulate state?
if a point lies in the interior of an angle, the measure of the entire angle is equal to the sum of the measures of the two smaller angles formed by the point.
This postulate helps in calculating angles when a point is located within an angle.
What is the Angle-Angle-Side (AAS) criterion for triangle congruence?
If 2 angles and the NON-INCLUDED side of 1 triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
What is the Angle-Side-Angle (ASA) criterion for triangle congruence?
If 2 angles and the INCLUDED side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
What does the Congruence/Measurement Postulate state?
Two line segments have the same measure if and only if they are congruent. Two angles have the same measure if and only if they are congruent.
What does the Converse of the Corresponding Angles Postulate state?
If two lines cut by a transversal form congruent corresponding angles, then the lines are parallel.
What is the Corresponding Angles Postulate?
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
What does the Hypotenuse-Leg (HL) criterion state?
If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.
What does the Segment Addition Postulate state?
If A, Z and B are collinear and Z is between A and B, then AZ + ZB = AB.
What is the Side-Angle-Side (SAS) criterion for triangle congruence?
If 2 sides and the INCLUDED angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
What does the Side-Side-Side (SSS) criterion state?
If 3 sides of one triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent.
What does the Midpoint Theorem state?
If B is the midpoint of segment AC, then AB = 1/2 AC.
What does the Overlapping Segment Theorem state?
If P, K, E and C are collinear and in that order, and PK = EC, then PE = KC.
What does the Alternate Exterior Angles Theorem state?
If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
What does the Converse of the Alternate Exterior Angles Theorem state?
If two lines cut by a transversal form congruent alternate exterior angles, then the lines are parallel.
What is the Alternate Interior Angles Theorem?
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
What does the Converse of the Alternate Interior Angles Theorem state?
If two lines cut by a transversal form congruent alternate interior angles, then the lines are parallel.
What is the Same Side Interior Angles Theorem?
If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
What does the Converse of the Same Side Interior Angles Theorem state?
If two lines cut by a transversal form supplementary same side interior angles, then the lines are parallel.
What does the Vertical Angle Theorem state?
If two lines intersect to form vertical angles, then the angles have equal measures.
What does the Pythagorean Theorem state?
The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
What does the Converse of the Pythagorean Theorem state?
If the sum of the squares of two sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle.
What does the Isosceles Triangle Theorem state?
If two sides of a triangle are congruent, then the two angles opposite those sides are congruent.
What does the Exterior Angle Theorem state?
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
What does the Triangle Angle Sum Theorem state?
The sum of the measures of the interior angles of a triangle is 180°.
