The diagonals of an isosceles trapezoid are congruent
2 answers:
Answer:
True.
Step-by-step explanation:
Please find the attachment.
We have been given a statement. We are supposed to determine whether the given statement is true or false.
Statement:
The diagonals of an isosceles trapezoid are congruent.
We know that an an isosceles trapezoid is a trapezoid in which base angles are equal and the left and right sides are equal as well.
We can form two congruent triangles (by SAS congruence) from an isosceles trapezoid as shown in the attachment.
Since two sides and including angle of triangle ADC is equal to two sides and including angle of triangle ADC is equal to BCD, therefore, both triangles are congruent.
By corresponding parts of congruent triangles are congruent, therefore, and our given statement is true.
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