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obj. 15 triangle angle relationships

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Obj. 15 Triangle Angle Relationships The student is able to (I can): • Classify triangles by sides and by angles • Find the measures of missing angles of right and equiangular triangles • Find the measures of missing remote interior and exterior angles

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Classify triangles by sides and by angles Find the measures of missing angles of right and equiangular triangles Find the measures of missing remote interior and exterior angles

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  • 1. Obj. 15 Triangle Angle Relationships The student is able to (I can): Classify triangles by sides and by angles Find the measures of missing angles of right and equiangular triangles Find the measures of missing remote interior and exterior angles

2. Classifying Triangles Triangles are classified by their side lengths and their angle measures as follows: By side length equilateral all sides congruent (equal) isosceles two sides congruent scalene no sides congruent By angle measure acute all acute angles right one right angle obtuse one obtuse angle equiangular all angles congruent 3. Practice Classify each triangle by its angles and sides. 1. 3. right equiangular scalene equilateral 902.4. 110acute isoscelesobtuse isosceles 4. Triangle Angle Sum Theorem All angles of a triangle add up to 180. Example: Find the measure of the missing angle5629180 (56 + 29) = 180 85= 95 5. corollaryA theorem whose proof follows directly from another theorem.Right Triangle CorollaryThe acute angles of a right triangle are complementary. ABmA+mB+mC=180 mA + 90 + mC = 180 mA + mC = 90C 6. Equiangular Triangle CorollaryThe measure of each angle of an equiangular triangle is 60. QE UmE = mQ = mU mE + mQ + mU = 180 mE + mE + mE = 180 3(mE) = 180 mE = 60 7. 2exteriorinterior 134interior angleThe angle formed by two sides of a polygonexterior angleThe angle formed by one side of a polygon and the extension of an adjacent sideremote interior An interior angle that is not adjacent to an angle exterior angle 8. 2exteriorinterior 1Exterior Angle Theorem34The measure of an exterior angle of a triangle is equal to the sum of its remote interior angles. m4 = m1 + m2 9. Third Angles TheoremIf two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. RELTA XR E 10. Practice 1. What is m1? 140140 = 105 + m1 m1 = 35 2. Solve for x 5x 60 = 2x + 3 + 15 5x 60 = 2x + 18 3x 60 = 18 3x = 78 x = 26105151(5x60) (2x+3)


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