Question

What is the quadrilateral? rhombus rectangle trapezoid square

Answer 1

A quadrilateral is a four-sided polygon, and a rhombus, rectangle, trapezoid, and square are all specific types of quadrilaterals, each with distinct properties that guide geometric calculations and problem-solving.

Step-by-step explanation:

The term quadrilateral refers to a four-sided polygon. Among the examples provided, rhombus, rectangle, trapezoid, and square are all types of quadrilaterals, each with its own unique properties.

A rhombus is a quadrilateral with all sides of equal length and opposite angles equal; a rectangle is a quadrilateral with four right angles and opposite sides equal; a trapezoid (or trapezium) is a quadrilateral with at least one pair of parallel sides; and a square is a special type of rectangle where all sides are equal in length, effectively combining the properties of both a rhombus and a rectangle.

These distinctions are made because each shape follows a specific set of geometric rules. For example, the sum of the interior angles in any quadrilateral is 360 degrees, not 180 degrees as it is for a triangle. Understanding these properties helps in the study of geometry and is essential for solving problems related to these shapes.

Answer 2

see below

Step-by-step explanation:

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.

A rhombus is a parallelogram with four congruent sides.

A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles.

A trapezoid is a quadrilateral with exactly one pair of parallel sides.