Question

3 from unit 2, lesson 13 abde is an isosceles trapezoid. ae≅bd ∠a≅∠b ∠e≅∠d priya makes a claim that triangle aeb is congruent to triangle is not true.

Explanation:

Step1: Recall properties of isosceles trapezoid

In isosceles trapezoid \(ABDE\), we have \(AE = BD\), \(\angle A=\angle B\) and \(\angle E=\angle D\), and \(AB\) is a common - side for \(\triangle AEB\) and \(\triangle BAD\).

Step2: Apply congruence criteria

By the Side - Angle - Side (SAS) congruence criterion, in \(\triangle AEB\) and \(\triangle BAD\), we have \(AE = BD\), \(\angle A=\angle B\), and \(AB = BA\) (reflexive property). So \(\triangle AEB\cong\triangle BAD\). But we need to check \(\triangle AEB\) and \(\triangle BDA\). Since we don't have enough information to prove \(\triangle AEB\cong\triangle BDA\) (the order of sides and angles matters in congruence statements). The claim that \(\triangle AEB\) is congruent to \(\triangle BDA\) may not be true. For example, if we consider the order of sides and angles for congruence rules like SSS, SAS, ASA, AAS, HL, we cannot match the corresponding parts correctly for \(\triangle AEB\) and \(\triangle BDA\) based on the given information about the isosceles trapezoid.

Answer:

The claim that \(\triangle AEB\) is congruent to \(\triangle BDA\) may not be true as we cannot satisfy the congruence criteria with the given information about the isosceles trapezoid.