Download Theorem 5-13 – The Hinge Theorem (SAS Inequality Theorem

Advanced Geometry
Topic 5 – Relationships within Triangles
NOTES – Inequalities in Two Triangles (5-8)
Name: _____________________________________________________
Date: _________________________________ Period: ____________
Theorem 5-13 – The Hinge Theorem (SAS Inequality Theorem)
Theorem
If…
Then…
If two sides of one triangle are congruent to
𝑚∠𝐴 > 𝑚∠𝑋
𝐵𝐶 > 𝑌𝑍
two sides of another triangle, and the
included angles are _________________
_________________, then the _________________
third side is opposite the _________________
included angle.
Theorem 5-14 – Converse of the Hinge Theorem (SSS Inequality)
Theorem
If…
Then…
If two sides of one triangle are congruent to
𝐵𝐶 > 𝑌𝑍
𝑚∠𝐴 > 𝑚∠𝑋
two sides of another triangle, and the
third sides are _________________
_________________, then the _________________
included angle is opposite the
_________________ third side.
Using the Hinge Theorem
Applying the Hinge Theorem
The diagram shows a pair of scissors in two different
positions. In which position is the distance between
the tips of the two blades greater? Use the Hinge
Theorem to justify your answer.
Using the Converse of the Hinge Theorem
What is the range of possible values for 𝑥 in the figure?
Proving Relationships in Triangles
STATEMENTS
REASONS
1)
𝑚∠𝑀𝑂𝑁 and 𝑚∠𝑀𝑂𝐿 are supp.
__________________ __________________ are supp.
2)
𝑚∠𝑀𝑂𝑁 + 𝑚∠𝑀𝑂𝐿 = 180
Definition of ________________________
3)
𝑚∠𝑀𝑂𝑁 = 80
4)
____________ + 𝑚∠𝑀𝑂𝐿 = 180
________________________ Property
5)
𝑚∠𝑀𝑂𝐿 = ____________
________________________ Property
6)
𝑚∠𝑀𝑂𝐿 > ____________
_______ > _______ ; ____________________ Property
7)
̅̅̅̅
O is the midpoint of 𝐿𝑁
8)
𝐿𝑂 = ____________
Definition of ________________________
9)
𝑀𝑂 = ____________
________________________ Property
10) 𝐿𝑀 > 𝑀𝑁
________________________ Theorem