Sec 2.6 Geometry-Triangle Proofs

Side-Angle-Side (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.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Definition of Perpendicular Lines

Lines that intersect to form right angles or 90°

Pythagorean Theorem

a²+b²=c²

CPCTC

corresponding parts of congruent triangles are congruent

Division Property of Equality

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

Multiplication Property of Equality

If a=b, then ac=bc

Definition of Midpoint

A point that divides a segment into two congruent segments

Definition of Supplementary Angles

2 angles whose sum is 180

Right Angle Theorem (RAT)

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 Equality

Any number is equal to itself (a=a)

Reflexive Property of Congruence

Figure A is congruent to figure A

Definition of Congruence

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

Segment Addition Postulate

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

Triangle Mid-segment Theorem

If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long.

Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

Transitive Property

If a=b and b=c, then a=c

Addition Property of Equality

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

Subtraction Property of Equality

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

Angle Addition Postulate

If point S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR.

Hypotenuse-Leg (HL)

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

Side-Side-Side (SSS)

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

Angle-Angle-Side (AAS)

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.

Angle-Side-Angle (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.

Linear Pair Theorem

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

Third Angles Theorem

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

Alternate Exterior Angles Converse Theorem

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

Corresponding Angles Converse

If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Triangle Sum Theorem

The sum of the measures of the angles of a triangle is 180.

Vertical Angle Theorem (VAT)

Vertical angles are congruent

Definition of Angle Bisector

a ray that divides an angle into 2 congruent angles