Get out a pencil and 2 pieces of paper. SILENTLY (that means without talking)… Get out a pencil and 2 pieces of paper. Start working on your warm-ups.

Learning Target: Students can find unknown angles in triangles. Math 8 Day 17 Learning Target: Students can find unknown angles in triangles.

Vocabulary Triangle Sum Theorem acute triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle

Draw a triangle and extend the bottom side Draw a triangle and extend the bottom side. Then draw a line parallel to the extended side, as shown. The sides of the triangle are transversals to the parallel lines. The three angles in the triangle can be arranged to form a straight line or 180°.

An acute triangle has 3 acute angles An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

Example 1: Find p° in the acute triangle. 73° + 44° + p° = 180° 117° + p° = 180° –117° –117° p° = 63°

Example 2: Find c° in the right triangle. 42° + 90° + c° = 180° 132° + c° = 180° –132° –132° c° = 48°

Example 3: Find m° in the obtuse triangle. 23° + 62° + m° = 180° 85° + m° = 180° –85° –85° m° = 95°

Example 4: Find a° in the acute triangle. 88° + 38° + a° = 180° 38° 126° + a° = 180° –126° –126° a° = 54° a° 88°

Example 5: Find b in the right triangle. 38° 38° + 90° + b° = 180° 128° + b° = 180° –128° –128° b° = 52° b°

Example 6: Find c° in the obtuse triangle. 24° + 38° + c° = 180° 38° 62° + c° = 180° 24° c° –62° –62° c° = 118°

Interior Angles Theorem: The sum of the interior angles of a triangle is ________°

An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

Example 7: Find the angle measures in the isosceles triangle. 62° + t° + t° = 180° Triangle Sum Theorem 62° + 2t° = 180° Combine like terms. –62° –62° Subtract 62° from both sides. 2t° = 118° 2t° = 118° 2 2 Divide both sides by 2. t° = 59° The angles labeled t° measure 59°.

Find the angle measures in the scalene triangle. Example 8: Find the angle measures in the scalene triangle. 2x° + 3x° + 5x° = 180° Triangle Sum Theorem 10x° = 180° Combine like terms. 10 10 Divide both sides by 10. x = 18° The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

Ticket Out the Door 1. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°. 2. Find the missing angle measure in an obtuse triangle with angle measures of 10° and 15°.