SOLUTION: How do you prove the base angles of an isoceles trapezoid are congruent?

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Question 202818: How do you prove the base angles of an isoceles trapezoid are congruent?
Answer by jsmallt9(3759)   (Show Source): You can put this solution on YOUR website!
Let's name the vertices of this triangle. Let's name them A, B and C and let's make A be the vertex where the two congruent sides meet. And let's draw a perpendicular segment from A to segment BC. Name the point where this perpendicular intersects segment BC point D. We now have two right triangles, triangle ADB and triangle ADC, inside triangle ABC. And angles ADB and ADC are right angles.

Here's the proof:
  1. Segment AB and Segment AC are congruent (Given)
  2. Segment AD is congruent to itself (Reflexive property of congruence)
  3. Angle ADB is congruent to Angle ADC (All right angles are congruent)
  4. Triangle ADB is congruent to triangle ADC (SSA (or HL))
  5. Angle ACB is congruent to Angle ABC (Corresponding parts of congruent triangles are congruent (CPCTC))

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