Triangle Sum Properties

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Presentation transcript:

Triangle Sum Properties Objective: -Classify triangles and find measures of their angles.

Classification By Sides Classification By Angles

Classifying Triangles In classifying triangles, be as specific as possible. Obtuse, Isosceles Acute, Scalene

Triangle Sum Theorem **NEW The sum of the measures of the interior angles of a triangle is 180o. 3 2 1 m<1 + m<2 + m<3 = 180°

60º 90º 30º 60º 180º 30º 90º Property of triangles The sum of all the angles equals 180º degrees. 60º 90º 30º + 60º 180º 30º 90º

40º 90º 40º 50º 180º 50º 90º Property of triangles The sum of all the angles equals 180º degrees. 40º 90º 40º 50º + 180º 50º 90º

60º 60º 60º 180º Property of triangles 60º 60º 60º The sum of all the angles equals 180º degrees. 60º 60º 60º 60º + 180º 60º 60º

What is the missing angle? 70º 70º ? + 180º 70º 70º 180 – 140 = 40˚

What is the missing angle? 90º ? 30º ? + 180º 30º 90º 180 – 120 = 60˚

What is the missing angle? 60º 60º ? + 60º 60º 180º 180 – 120 = 60˚

What is the missing angle? 30º 78º ? + 78º 30º 180º 180 – 108 = 72˚

Find all the angle measures B C A 180 = 35x + 45x + 10x 180 = 90x 2 = x 90°, 70°, 20°

What can we find out? 180 = 75 + 90 + x 180 = 165 + x 15 = x The ladder is leaning on the ground at a 75º angle. At what angle is the top of the ladder touching the building? 180 = 75 + 90 + x 180 = 165 + x 15 = x

Corollary to Triangle Sum Theorem A corollary is a statement that follows from a theorem. The acute angles of a right triangle are complementary. m∠A + m∠B = 90o

Find the missing angles. The tiled staircase shown below forms a right triangle. The measure of one acute angle in the triangle is twice the measure of the other angle. Find the measure of each acute angle. Con’t

Find the missing angles. SOLUTION: 2x + x = 90 3x = 90 x = 30˚ 2x = 60˚

Find the missing angles. 2x + (x – 6) = 90˚ 2x = 2(32) = 64˚ 3x – 6 = 90 3x = 96 (x – 6) = 32 – 6 = 26˚ x = 32

The End 