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