Chapter 6 Second Quiz Flashcards
Midsegment
A segment that connects the midpoints of two sides of a triangle.
Triangle Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the opposite side and half as long.
Midpoint Formula
X(1) + X(2) Y(1) + Y(2)
————– , —————
2 2
Triangle Relationship Theorem
If one side of a triangle is longer than another, then the opposite angle is longer and vice versa
Triangle Inequality Theorem
The sum of two SIDES of a triangle is always larger than the third SIDE.
Steps for an indirect proof
- Identify the proof statement
- Assume the opposite of the proof statement
- Work through proof until the given is contradicted
- Since the assumption of the proof statement is false, the opposite must be true
Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the 1st triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
Converse Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle, and the third side of the 1st triangle is larger than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.
Addition Property of Equality
If a>b and c> (or equal to) 0 then a+c > b+d
Multiplication Property of Equality
If a>b and c>0 then ac > bc
Division Property of Equality
If a>b and c>0 then a/c < b/c
Multiplication Property of Equality 2
If a>b and c<0 then ac < bc
Division Property of Equality 2
If a>b and c<0 then a/c < b/c
Transitive
If a > b and b > c then a > c
Note about Transitive
Don’t use substitution instead of transitive
