Unit 3 - Euclidean Triangle Proof Flashcards
Median of a Triangle
a line segment drawn from the vertex of a triangle to the midpoint of the opposite side
Altitude of a Triangle
a line segment drawn from the vertex of a triangle such that it is perpendicular to the opposite side
Addition Axiom
if equals are added to equals the sums are equal
Reflexive Axiom
a value is equal to itself (length or angle measure)
Subtraction Axiom
if equals are subtracted from equals, the differences are equal
S.A.S. Theorem
two triangles are congruent if two sides and the included angles are equal to anothers
A.S.A. Theorem
two triangles are congruent if a side and the adjacent angles of one are equal to anothers
S.S.S. Theorem
two triangles are congruent if three sides one are equal to anothers
CPCTC
Corresponding Parts of Congruent Triangles Are Congruent
if two triangles are congruent, then the sides and angles of those triangles must also be congruent
Axioms of Equality
- The Whole is the Sum of its Parts
- Addition
- Subtraction
- Substitution
Substitution
quantities equal to each other or to the same quantity may be substituted for each other
Complements of Equal Angles are Equal
&
Supplements of Equal Angles are Equal
Partitioning
breaking a segment or angle into parts or combining those parts
Exterior Angle Theorems
the measure of an exterior angle will ALWAYS be the sum of the remote interior angles
exterior angle is always bigger than an interior angle
Parallel Line Results
