GEOMETRY 5.5 INEQUALITIES involving 2 Triangles Pages: 273 – 275 Objectives: Learn and use the SAS Inequality Theorem Learn and use the SSS Inequality Theorem

GEOMETRY 5.5 SAS Inequality Theorem (Hinge) IF Two Sides of One Triangle are CONGRUENT, respectively, to Two Sides of a Second Triangle AND the INCLUDED Angle of the First Triangle is GREATER Than the INCLUDED angle of the Second, THEN The THIRD Side of the First Triangle is LONGER than the Third Side of the Second Triangle.

F GEOMETRY 5.5 E C A B D Given: Prove: AB > DE

GEOMETRY 5.5 U T 50 10 10 100 20 8 8 Y W X YU _______ XT

GEOMETRY 5.5 SSS Inequality Theorem IF -- Two SIDES of One Triangle are CONGRUENT, respectively, to Two Sides of a Second Triangle, AND the LENGTH of the Third Side of the First Triangle is GREATER than the Length of the Third Side of the Second Triangle THEN -- The ANGLE Opposite the Third Side of the First Triangle is GREATER than the Angle Opposite the Third Side of the Second Triangle.

GEOMETRY 5.5 D C 2 1 A B Given: Prove:

GEOMETRY 5.5 D 2 1 B C A Given: Prove:

P Q R 1 2 Given: S Prove:

GEOMETRY 5.5 S 4 3 1 2 R Q P

GEOMETRY 5.5 S 4 3 1 2 R Q P

GEOMETRY 5.5 S 4 3 1 2 R Q P

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GEOMETRY 5.5 Sometimes True Always True, or Never True? The Lengths of Two Sides of a Triangle are EQUAL, respectively, to the Lengths of Two sides of a Second Triangle, and the Third Side of the First Triangle is Longer than the Third Side of the Second Triangle.

GEOMETRY 5.5 GEOMETRY 5.5 Sometimes True Always True, or Never True? The Lengths of Two Sides of a Triangle are EQUAL, respectively, to the Lengths of Two sides of a Second Triangle, and the Third Side of the First Triangle is Longer than the Third Side of the Second Triangle. Sometimes True

GEOMETRY 5.5 Sometimes True Always True, or Never True? The Lengths of Two Sides of a Triangle are EQUAL, respectively, to the Lengths of Two Sides of a Second Triangle, the INCLUDED angle of the First Triangle is GREATER than the Included Angle of the Second Triangle, and the Third Sides are EQUAL in Length.

GEOMETRY 5.5 Sometimes True Always True, or Never True? The Lengths of Two Sides of a Triangle are EQUAL, respectively, to the Lengths of Two Sides of a Second Triangle, the INCLUDED angle of the First Triangle is GREATER than the Included Angle of the Second Triangle, and the Third Sides are EQUAL in Length. Never True

GEOMETRY 5.5 Sometimes True Always True, or Never True? The Legs of a Right Triangle are CONGRUENT, respectively, to the Legs of a Second Right Triangle, and the Hypotenuse of the First Right Triangle is LONGER than the Hypotenuse of the Second Right Triangle.

GEOMETRY 5.5 Sometimes True Always True, or Never True? The Legs of a Right Triangle are CONGRUENT, respectively, to the Legs of a Second Right Triangle, and the Hypotenuse of the First Right Triangle is LONGER than the Hypotenuse of the Second Right Triangle. Never True

P GEOMETRY 5.5 C D Q

GEOMETRY 5.5 You should be able to: State and use the SAS Inequality Theorem State and use the SSS Inequality Theorem Use the SAS and SSS Inequality Theorems in proofs Use the Inequality Theorems with the Biggest Angle – Longest Side Theorems to solve problems

GEOMETRY 5.5 Write a two-column proof. Given: Prove:

GEOMETRY 5.5 Given: Prove:

A. Write an inequality relating mLDM to mMDN using the information in the figure.

A. Compare mWYX and mZYW and write an inequality statement. A. mWYX < mZYW B. mWYX = mZYW C. mWYX > mZYW D. cannot be determined Lesson 5 CYP3

B. Find the range of values containing n and write an inequality statement. Lesson 5 CYP3