Question

select all of the quadrilaterals that have congruent diagonals. isosceles trapezoid square rhombus rectangle parallelogram this is a required question select all of the quadrilaterals whose diagonals are perpendicular to each other. isosceles trapezoid square rhombus rectangle parallelogram

Explanation:

First Question: Select ALL of the quadrilaterals that have congruent diagonals.

• Isosceles Trapezoid: By definition, the diagonals of an isosceles trapezoid are congruent.
• Square: A square is a special type of rectangle (and rhombus), and rectangles have congruent diagonals, so squares do too.
• Rhombus: In general, the diagonals of a rhombus are not congruent (unless it is a square). So a non - square rhombus has non - congruent diagonals.
• Rectangle: The diagonals of a rectangle are congruent (this can be proven using the Pythagorean theorem in the right triangles formed by the diagonals).
• Parallelogram: In a general parallelogram, the diagonals are not congruent. They bisect each other, but their lengths are equal only in special cases like rectangles.

• Isosceles Trapezoid: The diagonals of an isosceles trapezoid are congruent but not perpendicular.
• Square: A square is a special rhombus, and the diagonals of a rhombus are perpendicular. So the diagonals of a square are perpendicular.
• Rhombus: By the property of a rhombus, its diagonals are perpendicular bisectors of each other.
• Rectangle: The diagonals of a rectangle are congruent but not perpendicular (unless it is a square).
• Parallelogram: In a general parallelogram, the diagonals are not perpendicular. They bisect each other, but are perpendicular only in special cases like rhombuses.

Answer:

A. Isosceles Trapezoid, B. Square, D. Rectangle

Second Question: Select ALL of the quadrilaterals whose diagonals are perpendicular to each other.