Warmup 326 Announcements 1 Homework 6 1 Part

Announcements 1) Homework 6. 1 Part 2 due Today. 2) Homework 6. 2 due

Recall: - How many degrees are in a triangle? - Find the missing angle

Definitions An exterior angle of a triangle is an angle that forms a linear

Theorem 6. 6 Exterior Angle Theorem. The measure of an exterior angle of a

Ex #1 m∠MCB = m∠CBA + m∠BAC (17 x-6) = (8 x+6) + (60)

Ex #2 m∠CTU = m∠TUV + m∠UVT (24 x) = (90) + (9 x)

Ex #3 You find that for optimal sailing the angle for the front sail

Warm-up 3/27 5) What is the notation for line segment with endpoints A and

Announcements 1) Unit Quiz next Wednesday the 1 st 2) Period 3, Bring socks.

Cont of 6. 2 Exterior Angles and inequalities

Theorem 6. 7 Triangle Inequality. The sum of the lengths of any two sides

So why is it impossible to make a triangle where third side is equal

Ex #5 Can you make a triangle with side lengths 4, 8 and 11?

Slides: 16

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Warm-up 3/26

Announcements 1) Homework 6. 1 Part 2 due Today. 2) Homework 6. 2 due Monday 3) Unit Quiz next Wednesday the 1 st 4) Period 3, Bring socks. 3/26

6. 2 Exterior Angles and inequalities

Recall: - How many degrees are in a triangle? - Find the missing angle of the triangle. - Find x. Objective: Today we will learn how to find the measure using the exterior angle of triangles.

Definitions An exterior angle of a triangle is an angle that forms a linear pair with one of the angle so of the triangle. The remote interior angles of an exterior angle are the two angles of the triangle that do not form a linear pair with a given exterior angle.

Theorem 6. 6 Exterior Angle Theorem. The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. m∠QRT = m∠RST+ m∠STR

Ex #1 m∠MCB = m∠CBA + m∠BAC (17 x-6) = (8 x+6) + (60) 17 x-6 = 8 x+66 +6 +6 17 x = 8 x+72 -8 x 9 x = 72 ÷ 9 x=8

Ex #2 m∠CTU = m∠TUV + m∠UVT (24 x) = (90) + (9 x) -9 x 15 x = 90 Think: What will the ÷ 15 formula be to solve for x? x=6 Pair: You and your partner form a formula. Share: What was your formula?

Ex #3 You find that for optimal sailing the angle for the front sail must be set at a certain angle. You find that m∠ ABC =140°. If you know that m∠ BCD is three times as big as m∠ CDB, what should the angle of ∠ CDB be set to for optimal sailing? Think: What will the formula be to solve for m∠ CDB ? Pair: You and your partner form a formula and solve.

Warm-up 3/27 5) What is the notation for line segment with endpoints A and B? 6)What is the notation for the length of line segment with endpoints A and B?

Announcements 1) Unit Quiz next Wednesday the 1 st 2) Period 3, Bring socks. 3/27

Cont of 6. 2 Exterior Angles and inequalities

Theorem 6. 7 Triangle Inequality. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Ex #4 NM + MP > PN

So why is it impossible to make a triangle where third side is equal to the sum of the other two sides? Create a triangle with sides equal to 3 inches, 3 inches and 6 inches. Why is it impossible to make a triangle where third side is longer than the sum of the other two sides? Create a triangle with sides equal to 3 inches, 2 inches and 6 inches.

Ex #5 Can you make a triangle with side lengths 4, 8 and 11? NM + MP > PN 4 + 8 > 11 12 > 11, this is true so yes. Ex #6 Can you make a triangle with side lengths 23, 31, and 6? NM + MP > PN 6 + 23 > 31 29 > 31, this is false so no.