chivistaelmore

2022-07-24

Definition #1: an isosceles trapezoid is a trapezoid with exactly one pair of parallel sides and whose none parallel sides are congruent.
Definition #2: an isosceles trapezoid is a trapezoid with one pair of parallel sides and with the other pair of sides congruent.
a) Explain how isosceles trapezoid are related to rectangles under each Definition?
b) How are these Definitions related to the Definition of trapezoid ?
c) a quadrilateral has vertices at (-a,0), (a,0), (b,c) and (d,c). Under Definition #1, what conditions must be b and d satisfy if the quadrilateral is an isosceles trapezoid ? Under Definition #2, what conditions must be b and d satisfy if the quadrilateral is an isosceles trapezoid ?
d) Are the two Definitions equivalent? why or why not?

### Answer & Explanation

Brenton Gay

a) Isoceles trapezoids have one pair of parallel sides and other pair are congruent. It becomes a rectangle if the other pair of sides are perpendicular to given pair.
b) Neccessary condition for a trapezoid is one pair of sides must be parallel.teh case given is a particular case of trapezoid which is called isoceles trapezoid.
c) for an isoceles trapezoid, non parallel sides are congruent which means distnace between (-a,0) and (b,c) is equal to distance between (a,0)and (d,c)
(b+a)^2 + c^2 = (d-a)^2 + c^2
b +a = d- a
d - b =2a is the conditionthat b and d must satisfy

Alex Baird

d)Yes both the definitions are equivalent because non parallel sides are other pair of sides in a trapezoid.

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