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Geometry
Outline Sec. 5-7
Mrs. Sweet
Name:
Date:
Inequalities in One Triangle
What is the order of the distances between the hour and minute hands of a clock when the
times read:
1:00, 3:00, 5:00, 8:30, 1:30, 12:20?
When triangles have two pairs of congruent sides there is a special relationship between the
angles and the
pair of sides.
Hinge Theorem or SAS Inequality Theorem:
If two sides of one triangle are congruent
to two sides of another triangle, and the
included angles are not congruent, then the
third side is opposite
the
included angle.
Applying the Hinge Theorem:
EX. 1:
EX. 2: Which cheerleader’s hands are further apart?
Converse to the Hinge Theorem or SSS Inequality Theorem:
If two sides of one triangle are congruent
to two sides of another triangle, and the
included angles are not congruent, then the
included angle is opposite
the
third side.
Using the Converse to the Hinge Theorem:
EX. 3: What is the range of possible values for x in the figure below?
Proving Relationships in Triangles:
EX. 4:
EX. 5: