Download 5-5 Indirect Proof, triangle inequality, exterior angle inequality

Anna Chang
T2
Angle-Side Relationships in
Triangles
 The side that is opposite to the smallest angle will be
always the shortest side and the side that is opposite to
the largest angle will be the longest side
Examples
Smallest
to largest
<B, <A, <C
Indirect Proof
 At first, you assume that the statement is false and
then show that this causes a contradiction with facts
 Also called a proof by contradiction
Writing an Indirect Proof
1. Identify the conjecture to be proven
2. Assume the opposite of the conclusion is true
3. Use direct reasoning to show that the asssumption leads
to a contradiction
4. Conclude that since the assumption is false, the original
conjecture must be true
Examples
Q
p
R
Triangle inequality
 For the sum of the length of the two shorter sides must
always be longer than the third side (triangle)
Examples
Exterior angle inequality
 supplementary to the adjacent interior angle and it is
greater than either of the non adjacent interior angles.
Examples
Hinge Theorem
 If the two sides of two triangles are congruent but the
third side is not congruent then the triangle with the
longer side will have a larger included angle.
Converse of Hinge Theorem
 If two sides of one triangle are congruent to two sides
of another triangle and the third sides are not
congruent, then the larger included angle is across
from the longer third side.
Examples