1. Obj. 15 Triangle Angle RelationshipsThe student is able to (I can): Classify triangles by sides and by angles Find the measures of missing angles of right andequiangular triangles Find the measures of missing remote interior and exteriorangles

2. Classifying TrianglesTriangles are classified by their side lengths and their anglemeasures 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. PracticeClassify each triangle by its angles and sides.1. 3.902. 4.110rightscaleneequiangularequilateralacuteisoscelesobtuseisosceles 4. Triangle Angle Sum TheoremAll angles of a triangle add up to 180.Example: Find the measure of the missingangle56 29180 (56 + 29) = 180 85= 95 5. corollaryRight TriangleCorollaryA theorem whose proof follows directly fromanother theorem.The acute angles of a right triangle arecomplementary.AmA+mB+mC=180mA + 90 + mC = 180mA + mC = 90B C 6. EquiangularTriangleCorollaryThe measure of each angle of anequiangular triangle is 60.EQUmE = mQ = mUmE + mQ + mU = 180mE + mE + mE = 1803(mE) = 180mE = 60 7. interior angleexterior angleremote interiorangle12exterior3 4iiiinnnntttteeeerrrriiiioooorrrrThe angle formed by two sides of a polygonThe angle formed by one side of a polygonand the extension of an adjacent sideAn interior angle that is not adjacent to anexterior angle 8. Exterior AngleTheorem12The measure of an exterior angle of atriangle is equal to the sum of its remoteinterior angles.m4 = m1 + m23 4iiiinnnntttteeeerrrriiiioooorrrrexterior 9. Third AnglesTheoremIf two angles of one triangle are congruentto two angles of another triangle, then thethird pair of angles are congruent.XETLRAR @ E 10. Practice1. What is m1?2. Solve for x140105115(5x60)(2x+3)140 = 105 + m1m1 = 355x 60 = 2x + 3 + 155x 60 = 2x + 183x 60 = 183x = 78x = 26