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The properties of the trapezoid are as follows:
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The bases are parallel by definition.
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Each lower base angle is supplementary to the upper base angle on the same side.
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The properties of the isosceles trapezoid are as follows:
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The properties of a trapezoid apply by definition (parallel bases).
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The legs are congruent by definition.
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The lower base angles are congruent.
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The upper base angles are congruent.
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Any lower base angle is supplementary to any upper base angle.
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The diagonals are congruent.
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Here’s an isosceles trapezoid proof for you:
Statement 1:
Reason for statement 1: Given.
Statement 2:
Reason for statement 2: The legs of an isosceles trapezoid are congruent.
Statement 3:
Reason for statement 3: The upper base angles of an isosceles trapezoid are congruent.
Statement 4:
Reason for statement 4: Reflexive Property.
Statement 5:
Reason for statement 5: Side-Angle-Side, or SAS (2, 3, 4)
Statement 6:
Reason for statement 6: CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
Statement 7:
Reason for statement 7: If angles are congruent, then so are sides.