Presentation on theme: "5:4 Inequalities for Sides and Angles of a Triangle"— Presentation transcript:
15:4 Inequalities for Sides and Angles of a Triangle Objective: Recognize and apply relationships between sides and angles of triangles
2CTheorem: If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.EX.712AB9List the angles from greatestto least.
3EX:DTheorem: If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.35°55°EFList the sides from shortestto longest.
4EXAMPLE Which is greater, mCBD or mCDB? C Is mADB> mDBA? D Which is greater, mCDA or mCBA?C15D81216A10B
5PRACTICE Name the angle with the least measure in ▲LMN. Which angle in ▲MOT has the greatest measure?Name the greatest of the six angles in the two triangles, LMN and MOT.L10N76M95O8T
6EXAMPLE 1. Which side of ▲RTU is the longest? 2. Name the side of ▲UST that is the longest.3.T30º110ºRUS
7PRACTICE 1. What is the longest segment in ▲CED? 2. Find the longest segment in ▲ABE.3. Find the longest segment on the figure. Justify your choice.4. What is the shortest segment in BCDE?5. Is the figure drawn to scale? Explain.AE55ºD50º30º40º100ºCB
8Exit TicketFind the value of x and list the sides of ∆ABC in order for SHORTEST to LONGEST if the angles have the indicated measures.m∠A = 12x - 9, m∠B = 62 – 3x ,m∠C = 16x + 2