PLEASE HELP PLS I REALLLY NEED THE HELP WITH THIS Slope and the properties of perpendicular and parallel lines can be used to confirm that a polygon is a specific type of quadrilateral.

What types of quadrilaterals can you determine by using these properties? List at least two types of quadrilaterals.

Choose one type of quadrilateral from your answer to Question 1. Explain in complete sentences how you can use properties of perpendicular and parallel lines, together with slope, to confirm that a given polygon is the type of quadrilateral you chose. Be sure to clearly state the properties that you need to use.

Please number your responses to the questions as they are shown (1 and 2).

Picking apart the name “quadrilateral” helps you understand what it refers to. The prefix “quad-” means “four,” and “lateral” is derived from the Latin word for “side.” So a quadrilateral is a four-sided polygon. Since it is a polygon, you know that it is a two-dimensional figure made up of straight sides. A quadrilateral also has four angles formed by its four sides. Below are some examples of quadrilaterals. Notice that each figure has four straight sides and four angles. Interior Angles of a QuadrilateralThe sum of the interior angles of any quadrilateral is 360°. Consider the two examples below. You could draw many quadrilaterals such as these and carefully measure the four angles. You would find that for every quadrilateral, the sum of the interior angles will always be 360°. You can also use your knowledge of triangles as a way to understand why the sum of the interior angles of any quadrilateral is 360°. Any quadrilateral can be divided into two triangles as shown in the images below. In the first image, the quadrilaterals have each been divided into two triangles. The angle measurements of one triangle are shown for each. These measurements add up to 180º. Now look at the measurements for the other triangles—they also add up to 180º! Since the sum of the interior angles of any triangle is 180° and there are two triangles in a quadrilateral, the sum of the angles for each quadrilateral is 360°.

Geometric Properties of Quadrilaterals

a) Square

Opposite sides are parallel, with all sides being equal

Each of the angles is 90°

A square has four lines of symmetry

The order of rotational symmetry is 4

The diagonals bisect each other at 90° or right angles

b) Rectangle

The opposite sides are parallel and equal

All the angles in a rectangle are 90°

Lines of symmetry are two

Rectangle has a rotational symmetry of 2

c) Parallelogram

The opposite sides are parallel and equal

Parallelogram has equal opposite angles

There are no symmetry lines

Rotational symmetry order is 2

d) Kite

A kite has a single line of symmetry

The diagonals intersect at 90° or right angles

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