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1/15/20144-2: Measuring Angles in Triangles Expectations: G1.2.1: Prove that the sum of the angle measures of a triangle is 180 and that the measure of an exterior angle of a triangle is the sum of the measures of the 2 remote interior angles. G1.2.2: Solve problems involving angle measure and side length of triangles.

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1/15/20144-2: Measuring Angles in Triangles Linear Triples A, B and C form a linear triple iff A is adjacent to B, B is adjacent to C, A and C have no points in common (other than the vertex) and the sum of their measures is 180. A B C A, B and C form a linear triple.

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1/15/20144-2: Measuring Angles in Triangles Justify the sum of the measures of A, B and C. A B C

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1/15/20144-2: Measuring Angles in Triangles Triangle Sum Theorem: The sum of the measures of the angles of a triangle is _______°.

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1/15/20144-2: Measuring Angles in Triangles Determine the value of x. A C B 58 x - 8 x

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In triangle ABC below, the measure of A is 20° and the measure of B is 3 times larger than the measure of C. What is the measure of angle B? A.40° B.60° C.80° D.120° E.160° 1/15/20144-2: Measuring Angles in Triangles A B C

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1/15/20144-2: Measuring Angles in Triangles Calculate the measures of each angle below. 7x+3 5x+9 8x-12 A C B

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1/15/20144-2: Measuring Angles in Triangles A C B F E D If A D and C F, what may you conclude about B and E? Can you justify your conjecture?

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1/15/20144-2: Measuring Angles in Triangles

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1/15/20144-2: Measuring Angles in Triangles Third Angle Congruence Theorem: If two angles of one triangle are _____________ to 2 angles of a second triangle, then the third angles are also _____________.

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1/15/20144-2: Measuring Angles in Triangles Exterior Angles An angle is an exterior angle of a triangle iff it is the union of one side of the triangle and the extension of the other side that shares the same vertex as the first side.

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1/15/20144-2: Measuring Angles in Triangles Exterior Angles AB C D CBD is an exterior angle for ABC

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1/15/20144-2: Measuring Angles in Triangles Exterior Angles AB C E ABE is an exterior angle for ABC

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1/15/20144-2: Measuring Angles in Triangles Exterior Angles Because there are 2 exterior angles at each vertex, every triangle has a total of 6 exterior angles.

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1/15/20144-2: Measuring Angles in Triangles Remote Interior Angles: A remote interior angle of a triangle is one of the 2 interior angles not adjacent to an exterior angle. Remote interior angles change depending on which interior angle is being discussed.

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1/15/20144-2: Measuring Angles in Triangles A C B D Remote Interior Angles: __ and __ are remote interior angles for exterior BCD.

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1/15/20144-2: Measuring Angles in Triangles A C B E Remote Interior Angles: __ and __ are remote interior angles for exterior BAE.

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1/15/20144-2: Measuring Angles in Triangles Exterior Angle Theorem: The measure of an exterior angle of a triangle is the sum of the measures of

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1/15/20144-2: Measuring Angles in Triangles Exterior Angle Theorem: A Proof A C B D Given: Δ ABC with exterior angle BCD Prove: m BCD = m A + m B

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1/15/20144-2: Measuring Angles in Triangles Given: ΔABC with exterior angle BCD Prove: m BCD = m A + m B A C B D

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1/15/20144-2: Measuring Angles in Triangles What is the measure of A? 124° A 52°

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1/15/20144-2: Measuring Angles in Triangles A corollary is a theorem that is easily proven by another theorem. Corollary

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1/15/20144-2: Measuring Angles in Triangles Acute Angles Corollary The acute angles of a right triangle are ____________. A C B m A + m B =

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1/15/20144-2: Measuring Angles in Triangles Right Angle Corollary There can be at most ___ right angle in a triangle. Obtuse Angle Corollary There can be at most ___ obtuse angle in a triangle.

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1/15/20144-2: Measuring Angles in Triangles In triangle ABC, m A is 16 more than m B and m C is 29 more than m B. Determine the measure of each angle.

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1/15/20144-2: Measuring Angles in Triangles

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1/15/20144-2: Measuring Angles in Triangles If AB is perpendicular to BC, determine the measures of all 8 numbered angles.

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1/15/20144-2: Measuring Angles in Triangles Assignment: pages 193-195, # 15-19 (odds), 36, 39, 42-44 (all)

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