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Q: Quadrilateral with one diagonal that divides it into two congruent equilateral triangles?

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Square

Yes, it can be split into two equilateral triangles,when we draw a diagonal

A heptagon has 4 diagonal lines and 7 sides and it has 2 congruent diagonal lines and 2 congruent triangles

a quadrilateral in which diagonal are not congruent and larger diagonal is perpendicular bisector of smaller diagonal then it is known as kite

No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.

Related questions

none the diagonal will always be bigger than a side

Yes

Square

False. A diagonal of a parallelogram produces 2 congruent triangles

Yes, it can be split into two equilateral triangles,when we draw a diagonal

Answer: 2 Explanation: A parallelogram is a quadrilateral which has both pairs of the opposite sides parallel. Congruent triangles are triangles that have exactly the same three sides and exactly the same three angles. So, in a parallelogram, each diagonal divides it in 2 congruent triangles. Source: Algebra.com

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A quadrilateral in which diagonal are not congruent and only larger diagonal is perpendicular bisector of smaller diagonal then it is known as kite -- Mohan S. Vighe

draw a diagonal through opposite corners of the quadrilateral. This makes two triangles. Prove the triangles are congruent using SSA (side side angle) congruence. Then show that the other two sides of the quadrilater must be congruent to each other, so it is a parallelogram.

A Rhombus. If it makes two equilateral triangles with a diagonal, the shape must have all four sides of equal length; thus it is a rhombus, possibly a square. As an equilateral triangle is made, the angle between two of the sides is 60o; which is not 90o, so it can't be a square, so it must be a rhombus.

A heptagon has 4 diagonal lines and 7 sides and it has 2 congruent diagonal lines and 2 congruent triangles

Two triangles

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