Understanding Isosceles Trapezoids

This video tutorial explains how to determine if a quadrilateral is an isosceles trapezoid. It covers the criteria for identifying isosceles trapezoids, such as congruent legs, base angles, and diagonals. The video includes two example problems with detailed two-column proofs, demonstrating the use of congruent triangles and the angle-angle-side postulate to establish the isosceles trapezoid properties.

Which of the following is NOT a condition to prove a quadrilateral is an isosceles trapezoid?

• The opposite angles are congruent.

• The diagonals are congruent.

• The lower base angles are congruent.

• The legs of the trapezoid are congruent.

In the first example, which angles are given as congruent?

• Angle CAD and Angle BDA

• Angle ABD and Angle DCA

• Angle AEB and Angle DEC

• Angle BAC and Angle CDE

What property is used to prove that vertical angles are congruent?

• Angle-Side-Angle Postulate

• Vertical Angles Theorem

• Transitive Property

• Reflexive Property

Which postulate is used to prove the congruence of triangles in the first example?

• Side-Angle-Side Postulate

• Angle-Angle-Side Postulate

• Angle-Side-Angle Postulate

• Side-Side-Side Postulate

What does CPCTC stand for?

• Corresponding Parts of Congruent Triangles are Congruent

• Congruent Parts of Corresponding Triangles are Congruent

• Corresponding Parts of Congruent Triangles are Equal

• Congruent Parts of Corresponding Triangles are Equal

In the second example, which angles are initially given as congruent?

• Angle BAC and Angle CDE

• Angle DCA and Angle ABD

• Angle AEB and Angle DEC

• Angle CAD and Angle BDA

What common side is shared by the triangles in the second example?

• Side AB

• Side BD

• Side AC

• Side AD

Which postulate is used to prove the congruence of triangles in the second example?

• Side-Angle-Side Postulate

• Angle-Angle-Side Postulate

• Angle-Side-Angle Postulate

• Side-Side-Side Postulate

What is the final step to prove that a quadrilateral is an isosceles trapezoid in the second example?

• Prove the opposite sides are congruent

• Prove the base angles are congruent

• Prove the diagonals are congruent

• Prove the legs are congruent

What is the definition of an isosceles trapezoid used in the examples?

• A trapezoid with congruent base angles

• A trapezoid with congruent legs

• A trapezoid with congruent opposite sides

• A trapezoid with congruent diagonals