Theorems, Postulates, and Properties

27 terms

Adding same number to each side of an equation makes it equivalent

Subtraction Property of Equality

Subtracting same number to each side of an equation makes it equivalent

Multiplication Property of Equality

Multiplying same number to each side of an equation makes it equivalent

Division Property of Equality

Dividing same number to each side of an equation makes it equivalent

AB +BC= AC

angle RSP + angle PST = angle RST

Reflexive Property of Congruence

A is congruent to A

Symmetric Property of Congruence

A is congruent to B and B is congruent to A

Transitive Property of Congruence

AB is congruent BC and BC is congruent to CD, so AB is congruent to CD

A equals A

Symmetric Property of Equality

A equals B and B equals A

Transitive Property of Equality

AB equals BC and BC equals CD, so AB equals CD

Right Angle Congruence Theorem

All Right Angles are congruent

Congruent Supplement Theorem

If 2 angles are supplementary to the same angle, then they are congruent

Congruent Complement Theorem

If 2 angles are complementary to the same angle, then they are congruent

Linear Pair Postulate

If 2 angles form a linear pair, then they are supplementary

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If a line intersects another line to form two supplementary angles, then the lines are perpendicular

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If two lines are perpendicular , then they intersect to form four right angles

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If two adjacent angles's sides are perpendicular then they are complementary

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

Lines Perpendicular to a Transversal Theorem

If two lines are perpendicular to the same line, then they are parallel to each other.

SSS Congruence Postulate

3 sides are congruent to 3 corresponding , then the triangles are congruent

SAS Congruence Postulate

a side, angle and side are congruent to a side, angle, and side of another triangle then the triangles are congruent

HL Congruence Theorem

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

ASA Congruence Theorem

An angle, side, and an angle are congruent to angle side and angle of another triangle then the triangles are congruent

AAS Congruence Theorem

Angle Angle and side and congruent to Angle Angle and side of another triangle then the triangles are congruent

Alternate Interior Angles Theorem

2 parallel lines are cut by transversal, the alternate interior angles are congruent