Question

NO LINKS!! URGENT HELP PLEASE!!​

Answer 1

a) Must be a rhombus.
Could be a square, a rectangle, a parallelogram, a trapezoid, or a kite.

b) Must be a parallelogram.
Could be a square, a rectangle, a kite, or a rhombus.

c) Must be a rectangle.
Could be a square, a kite, a rhombus or a parallelogram.

Step-by-step explanation:

The six basic types of quadrilaterals are:

• Square: All interior angles are 90°. Side lengths are equal.
• Rectangle: All interior angles are 90°. Opposite sides lengths are equal.
• Rhombus: Side lengths are equal.
• Trapezoid: One pair of parallel sides.
• Parallelogram: Opposite sides are parallel.
• Kite: Two pairs of equal length sides (these sides are adjacent to each other).

a) "My quadrilateral has four equal sides"

A quadrilateral by definition is a four-sided shape. Therefore, it is possible for all types of quadrilateral to have four equal sides. However, for it to be a square and a rhombus, it must have four equal sides.

The interior angles of a square are all right angles, and its opposite sides are parallel. So as we haven't been told anything about the interior angles of the quadrilateral, or if any of its sides are parallel, we can conclude that:

• The quadrilateral must be a rhombus.

• The quadrilateral could be a square, a rectangle, a parallelogram, a trapezoid, or a kite.

b) "My quadrilateral has two sets of parallel sides"

The types of quadrilateral that can have two sets of parallel sides are square, rectangle, rhombus, parallelogram and kite (all squares are kites).

The interior angles of a square and a rectangle are 90°.

The side lengths of a rhombus are congruent.

As we haven't been told anything about the interior angles or the side lengths of the quadrilateral, we can conclude that:

• The quadrilateral must be a parallelogram.

• The quadrilateral could be a square, a rectangle, a kite, or a rhombus.

c) "My quadrilateral has four right angles"

All quadrilaterals, apart from a trapezium, can have interior angles that are all right angles. However, for a quadrilateral to be a square or a rectangle, it must have interior angles that are right angles.

As we don't know if the side lengths of the quadrilateral are equal, we cannot know if it's a square. Therefore, we can conclude that:

• The quadrilateral must be a rectangle.

• The quadrilateral could be a square, a kite, a rhombus or a parallelogram.

Answer 2

a. My quadrilateral has four equal sides.

Must be: Rhombus.

Could be: Square.

b. My quadrilateral has two sets of parallel sides.

Must be: Parallelogram.

Could be: Rectangle, Rhombus, Square

c. My quadrilateral has four right angles.

Must be: Rectangle.

Could be: Square.

Step-by-step explanation:

• a. A quadrilateral with four equal sides must be a rhombus. It could also be a square, but a square is a special type of rhombus, so a rhombus is the "must be" shape.

b. A quadrilateral with two sets of parallel sides must be a parallelogram. It could also be a rectangle, a rhombus, or a square. However, a rectangle, rhombus, or square is also a parallelogram, so a parallelogram is the "must be" shape.

c. A quadrilateral with four right angles must be a rectangle. It could also be a square, but a square is a special type of rectangle, so a rectangle is the "must be" shape.