6.5 Inequalities for Two Triangles

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Presentation transcript:

6.5 Inequalities for Two Triangles Geometry 6.5 Inequalities for Two Triangles

SAS Inequality Theorem If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger 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. Imagine a stick in the crocodile’s mouth. What would the crocodile do to fit a longer stick in her jaws? BIG BIG She cannot lengthen her jaws, they are the congruent side of the triangle. She can, however, change the included angle of the two sides of her jaw, therefore making the side opposite that angle bigger. small small Therefore, the stick (the third side) would be longer.

SSS Inequality Theorem If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is larger than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second triangle. BIG small BIG small

Examples: What can you deduce from the given information Examples: What can you deduce from the given information? What theorem applies? 1.  D is the midpoint of AC  m1 < m2 2.  AB  CD 4. A B C D 2 1 G E O S 6 7 3. A B C D 1 2 3.05 4.1  mDCB > mABC

Examples: What can you deduce from the given information Examples: What can you deduce from the given information? What theorem applies? 5. 6. 7. 8. A B C D 12 42 43 6 8 A 3 B A B C D 3x 5x 6 7 1 2

HW P. 230-232 CE (#1-8) WE (#1-11)

What can you deduce from the given information What can you deduce from the given information? Name the theorem that supports your answer. GIVEN: B D is the midpoint of AC. BIG small 7 m 1 < m 2 7 small BIG 1 2 A D C ANSWER: AB < BC By SAS Ineq. Thm.

What can you deduce from the given information What can you deduce from the given information? Name the theorem that supports your answer.THIS SLIDE MAY BE INCORRECT E small 6 6 BIG O G BIG small 7 6 S ANSWER: m GSE < m SEO 7 7 By SSS Ineq. Thm.

What can you deduce from the given information What can you deduce from the given information? Name the theorem that supports your answer. BIG GIVEN: BIG AB = CD 7 m DCB > m ABC 7 C C D small small A A B B ANSWER: DB > AC By SAS Ineq. Thm.

What can you deduce from the given information What can you deduce from the given information? Name the theorem that supports your answer. 6 8 BIG small 6 3 6 BIG small A B 6 6 ANSWER: m A > m B 7 7 By SSS Ineq. Thm.

What can you deduce from the given information What can you deduce from the given information? Name the theorem that supports your answer. small 80 BIG 100 1 50 50 2 40 40 small 6 7 BIG But how does that affect the measures of angles 1 and 2? Let’s throw in some possible measurements! ANSWER: m 1 > m 2 7 7 By SSS Ineq. Thm. And Iso. Triangle Thm.

A Few From the HW P. 230 #5 P. 231 #3