The Third Side William L. Ury Harvard University. The Challenge. What will it take to transform destructive conflict into constructive conflict at home, at work, in the community & in the world?. Two Sides of the Conflict. Side 1. Side 2. The Third Side of the Conflict. Side 3.

ByThe Hinge Theorem. The Hinge Theorem If two sides of a 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 of the first is longer than the third side of the second.

ByEXAMPLE 3. Find possible side lengths. ALGEBRA. A triangle has one side of length 12 and another of length 8 . Describe the possible lengths of the third side. SOLUTION.

ByObjectives. State the inequalities that relate angles and lengths of sides in a triangle State the possible lengths of three sides of a triangle. Angle-Side Relationships in a Triangle. If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

ByLesson 8.6. Proportions and Similar Triangles. Lesson 8.6 Objectives. Identify proportional components of similar triangles Use proportionality theorems to calculate segment lengths. Theorem 8.4: Triangle Proportionality

ByLesson 5.1 Midsegment Theorem and Coordinate Proof. B. E. D. C. A. Vocabulary. The Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle. D and E are midpoints. DE is the midsegment. B. E. D. C. A. Theorem 5.1. Midsegment Theorem.

ByPythagorean triples. Who was Pythagoras?. Pythagoras was a bully!. He lived in Greece from about 580 BC to 500 BC. He is most famous for his theorem about the lengths of the sides in right angled triangles. What are Pythagorean Triples?.

ByThe inverse trigonometric functions. The inverse trigonometric functions The reciprocal trigonometric functions Trigonometric identities Examination-style question. Contents. 1 of 35. © Boardworks Ltd 2006. The inverse of the sine function.

By5.5 Inequalities in Triangles. Chapter 5 Relationships Within Triangles. Theorem 5-10. If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. Y. 11. 12. X. 14. Z. <Y is the largest angle. Comparing Angles.

By5.3 Proving Triangle Similar. Postulate 15: If the three angles of one triangle are congruent to the three angles of a second triangle, then the triangles are similar (AAA)

ByWarm up question: You are presented with five cards shown as follows: Given that each card has one letter on one side and one number on the other side, which cards need to be flipped in order to determine the validity of the following statement:

ByParallel Lines and Proportional Parts. Section 7.4. Proportional parts of triangles. Non parallel transversals that intersect parallel lines can be extended to form similar triangles. So, the sides of the triangles are proportional. Side Splitter Theorem or Triangle Proportionality Theorem.

By5.3 Proving Triangle Similar. Postulate 15: If the three angles of one triangle are congruent to the three angles of a second triangle, then the triangles are similar (AAA)

ByAB DE. BC EF. m B > m E. Proof : Assume temporarily that m B > m E . Then, it follows that either m B = m E or m B < m E . EXAMPLE 4. Prove the Converse of the Hinge Theorem. Write an indirect proof of Theorem 5.14 . GIVEN :. AC > DF. PROVE:.

ByMidsegments of Triangles 5.1. Today’s goals By the end of class today, YOU should be able to…. 1. Define and use the properties of midsegments to solve problems for unknowns. 2. Use the properties of midsegments to make statements about parallel segments in a given triangle.

ByExample: Working with Fractions. Solving Applied problems . PROBLEM. Adam wants to fence a triangular shaped yard. He wants to determine how many feet of fencing he will need. The sides of his yard measure as shown in the diagram below. How many feet of fencing should Adam buy? . 7 ½ ft.

ByOur last new Section…………5.6. The Law of cosines. Deriving the Law of Cosines. C ( x , y ). C ( x , y ). a. b. b. a. c. A. B ( c ,0). c. A. B ( c ,0). C ( x , y ). In all three cases:. a. b. Rewrite:. c. A. B ( c ,0). Deriving the Law of Cosines. C ( x , y ).

By7.1 Law of Sines Day 1. Do Now Let Triangle ABC be a right triangle where angle C is 90 degrees, angle B is 37.1 degrees, and side BC is 6.3 Solve the triangle. Test Review. Retakes by . Solving Triangles.

ByWelcome to Final Review Jeopardy!. With your host, Mrs. Barnes. TRIG. TRIG. TRIG. TRIG. TRIG. 5 pt. 5 pt. 5 pt. 5 pt. 5 pt. 10 pt. 10 pt. 10 pt. 10 pt. 10 pt. 15 pt. 15 pt. 15 pt. 15 pt. 15 pt. 20 pt. 20 pt. 20 pt. 20 pt. 20 pt. 25 pt. 25 pt. 25 pt. 25 pt. 25 pt.

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