Classifying Triangles And The Triangle Sum Theorem.

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Presentation transcript:

Classifying Triangles And The Triangle Sum Theorem

Warm-Up 1. Name 2 pair of alternate interior angles <5 & <3 and <4 & <1 2.What is the sum of m<1 + m<2 + m<3? 180° 3. If m<4 = 65° and m<5 = 50°, what is m<2? 65°

Warm Up Find the value of the indicated angles. Justify.

Classification By Angles

Classification By Sides

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

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

The sum of all the angles equals 180º degrees. 90º 30º 60º 90º 30º + 180º Sum of the angles in a triangle

What is the missing angle? (I Do) 70º + 140º 70º ? 180 – 140 = 0˚

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

60º + 120º 60º ? 180 – 120 = 60˚ What is the missing angle? (You Do)

45x 10x 35x Find all the angle measures 35x + 45x + 10x = x = 180 x = 2 Finally, plug in the value of x to find each angle measure.

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

The tiled staircase shown below forms a right triangle and the largest acute angle is twice as big as the smaller acute angle. Find the measure of angle. Find the missing angles. Continued on next slide

Find the missing angles. 2x + x = 90 3x = 90 SOLUTION: x = 30 The smallest acute angles measures: The largest acute angle measures:

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