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What is the difference between an isosceles trapezoid and an isosceles triangle?
An Isosceles trapezoid has four sides (is a quadrilateral) with a pair of parallel sides and the other two sides of equal length; whereas An isosceles triangle has three sides with a pair of sides of the same length and the other side a different length.
How many pair of parallel lines is equilateral triangle?
None. A triangle (not even an equilateral one) has no parallel sides.
What type of Quadrilateral has exactly one pair of parallel sides?
Trapezoids have only one pair of parallel sides.
If orthocentre and circumcentre of a triangle coincide then is it an equilateral triangle?
Yes. The orthocenter is the intersection of the altitudes; the circumcenter is the intersection of the perpendicular bisectors of the three sides of the triangle. The perpendicular bisector of and altitude to a given side are parallel, so they can coincide at the common center only if they are the same; that means that the opposite vertex is on the perpendicular bisector, so the other two sides are equal. Thus each pair of sides are equal, so the triangle is equilateral.
Do all trapezoids have exactly one pair of congruent sides?
By definition, a trapezoid only must have exactly one pair of parallel sides. An isosceles trapezoid does have one pair of congruent sides, but not all trapezoids will have exactly one pair of congruent sides.
