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In an isosceles triangle, the two angles opposite the congruent sides are called the base angles. You may have learned in a previous course that the base angles of an isosceles triangle are always congruent. Now you will prove it! In the diagram at right, is an isosceles triangle, and point is the midpoint of .

Triangle, M,S,Y, with line segment drawn from the vertex, Y, perpendicular to the opposite side, SM, at E, creating 2 internal triangles, S,Y,E, & M,Y,E, labeled as follows: Side, SY, 1 tick mark, side, M,Y, 1 tick mark. Side, SE, 2 tick marks, side, EM, 2 tick marks.

  1. ​Make a flowchart to prove that the base angles of are congruent, that is, prove that .

    Flow Chart: 5 ovals: #1,2,3, flow to #4, #4 flows to #5. Labels: #1: YS, congruent to, YM, & Given, definition of isosceles. #2: YE, congruent to, YE, & segment is congruent to itself. #3: SE, congruent to, EM, & definition of midpoint. #4: Triangle, Y,E,S, congruent to triangle, Y,E,M, & S,S,S, congruence. #5: angle S, congruent to angle M, & congruent triangles give congruent parts.

  1. Would your proof work for any isosceles triangle? State your findings as an if-then statement and add it to your Theorem Graphic Organizer.

    Since we found this to be true, formulate an if-then statement to conclude information from the flowchart.