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The sum of the angles for any triangle is 180 degrees. If we know two angles, we can total and subtract from 180 to get the missing angle. Find the missing angle measurement. 23 o o 39 o 180 - 62 118 39 + 23 62The sum of the angles for any triangle is 180 degrees. If we know two angles, we can total and subtract from 180 to get the missing angle. Find the missing angle measurement. 40 o o The longest side of a triangle is always directly across from the largest angle. The shortest side of the triangle is always directly across from the smallest angle. The medium side is directly across from the medium angle. Name the medium side. C 23º A 118º AB BC AC 39º B The longest side of a triangle is always directly across from the largest angle. The shortest side of the triangle is always directly across from the smallest angle. The medium side is directly across from the medium angle. Name the shortest side. D 53º 60º F 67º E DE EF DF The longest side of a triangle is always directly across from the largest angle. The shortest side of the triangle is always directly across from the smallest angle. The medium side is directly across from the medium angle. Name the longest side. L 53º 60º 67º M N LN LM NM Can the following be the side lengths of a triangle? The Triangle Inequality Theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the length of the third side. {6, 8, 13} Yes Not enough information No Can the following be the side lengths of a triangle? The Triangle Inequality Theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the length of the third side. {2, 12, 9} Yes Not enough information No Can the following be the side lengths of a triangle? The Triangle Inequality Theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the length of the third side. {15, 7, 8.5} Yes Not enough information No The three sides of a triangle are {10, x, 8}.Which inequalities can be written? Select two! The Triangle Inequality Theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the length of the third side. x + 8 > 10 8 + 10 ≥ x 10 + x > 8 10 + 8 > x x > 10 + 8 The three sides of a triangle are {10, x, 8}Write a compound inequality that shows the range of possible values for x. The Triangle Inequality Theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the length of the third side. < x < The three sides of a triangle are {3, 10, x}.Write a compound inequality that shows the range of possible values for x. The Triangle Inequality Theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the length of the third side. < x < Exterior Angles of Triangles Theorem: A measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles. Example: (77 + 90)º 13º 77º Exterior Angle Theorem: A measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles. Find the measure of the exterior angle of the triangle. o 103º 51º Exterior Angle Theorem: A measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles. Find the measure of the exterior angle of the triangle. o º 95º 65º Exterior Angle Theorem: A measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles. Find the measure of the interior angle of the triangle. 165º 88º o Find the measure of the interior angle of the triangle. Exterior Angle Theorem: A measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles. 16º o 108º The hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. Compare sides AC and DF. Example: AC > DF Compare angles A and D. m∠D m∠A Select the inequality that can be written using the diagram: 2x + 5 ≤ 66 2x + 5 < 66 2x + 5 > 66 2x + 5 ≥ 66 Select the inequality that can be written using the diagram: 50 2x 2x > 50 2x ≤ 50 2x ≥ 50 2x < 50 |