Geometry
Day 4 Notes: Inequalities in Two Triangles
Name_________________________
Warm Up
Name the shortest and longest sides of the triangle.
1.
2.
Solve the inequality AB + AC > BC for x
3.
The Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle,
and the included angle of the first is larger than the included angle of the
second, then the third side is ________ the third side of the second.
Converse of the Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle,
and the third side of the first is longer than the third side of the second,
then the included angle of the first is _______ than the included angle of
the second.
Example #1
Given that ̅̅̅̅
𝑨𝑫 ≅ ̅̅̅̅
𝑩𝑪, how does 1 compare to 2 ?
Example #2
̅̅̅̅𝒐𝒓 ̅̅̅̅
If mADB  mCDB , which is longer, 𝑨𝑩
𝑪𝑩?
Example #3
Complete the statement with <, >, or =. Explain.
a. JL ____ ST
b. m DEG ____ m FEG
Example #4
Using only the Hinge Theorem or its converse, write and solve an inequality to describe a restriction on
the value of x.
Example #5
You and a friend walk away from a tree in opposite directions. You both walk 20 yards, then change
direction and walk 5 yards. You start due east and then turn 45° to ward north. Your friend starts due
west and then turns 40° toward south. Who is farther from the tree?
Begin by drawing a diagram.