Triangle Proofs Vocabulary

Isosceles Triangle Theorem (and converse)

A triangle is isosceles if and only if its base angles are congruent

Pythagorean Theorem (and converse)

A triangle is right triangle if and only if the given the length of the legs a and b and hypotenuse c have the relationship a^2+b^2=c^2

Side-Angle-Side Postulate (SAS)

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

Definition of Perpendicular Lines

Lines that intersect to form right angles or 90 degrees

Division Property of Equality

If a=b, then a/c=b/c

Multiplication Property of Equality

If a=b, then ac=bc

Triangle Mid-segment Theorem

A mid-segment of a triangle is parallel to a side of the triangle, and its length is half the length of that side

Right Angle Theorem (R.A.T)

All right angles are congruent

Definition of a Straight Line

An undefined term in geometry, a line is a straight path that has no thickness and extends forever. It also forms a straight angle which measures 180 degrees

Reflexive Property of Congruence

Any figure is congruent to itself (Figure A is congruent to Figure A)

Reflexive Property of Equality

Any measure is equal to itself (a=a)

Definition of Supplementary Angles

Any two angles that have a sum of 180 degrees

Alternate Exterior Angle Theorem (and converse)

Are congruent if and only if the transversal that passes through two lines that are parallel

Alternate Interior Angle Theorem (and converse)

Are congruent if and only if the transversal that passes through two lines that are parallel

Corresponding Angle Theorem (and converse)

Are congruent if and only if the transversal that passes through two lines that are parallel

Same-Side Interior Angles (and converse)

Are supplementary if and only if the transversal that passes through two lines that are parallel

CPCTC

Corresponding Parts of Congruent Triangles are congruent by definition of congruence

Definition of Congruence

Having the exact same size and shape and there by having the exact same measures

Hypotenuse-Leg Postulate (HL)

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

Addition Property of Equality

If a=b, then a+c=b+c

Subtraction Property of Equality

If a=b, then a-c=b-c

Segment Property of Equality

If point B is between Point A and C then AB+BC=AC

Angle Addition Postulate

If point S is in the interior of angle PQR, then the measure of angle SQR= the measure of angle PQR

Side-Side-Side Postulate (SSS)

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

Angle-Side-Angle Postulate (ASA)

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

Angle-Angle-Side Postulate (AAS)

If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent

Linear Pair Theorem

If two angles from a linear pair then they are adjacent and supplementary

Third Angle Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent

Definition of Angle Bisector

The Ray that divides an angle into two congruent angles

Definition of Midpoint

The point that divides a segment into two congruent segments

Triangle Sum Theorem

The three angles of a triangle sum to 180 degrees

Vertical Angle Theorem (V.A.T)

Vertical angles are congruent