# Lesson 4 Symmetries of Quadrilaterals Develop Understanding

### 1.

Define a polygon.

### 2.

Fill in the names of each polygon based on the number of sides the polygon has.

Number of Sides | Name of Polygon |
---|---|

### 3.

One quadrilateral with special attributes is a kite. Find the geometric definition of a kite and write it below along with a sketch.

### 4.

Draw a kite and include all of the lines of reflective symmetry and all of the diagonals.

line of reflective symmetry:

diagonals:

### 5.

List any rotational symmetry for a kite.

Consider quadrilaterals such as parallelogram, rectangle, square, rhombus, and kite for the following questions.

### 6.

Are lines of symmetry also diagonals for any given polygon? Explain.

### 7.

Are all diagonals also lines of symmetry for any given polygon? Explain.

### 8.

Which quadrilaterals have diagonals that are not lines of symmetry? Name some and draw them.

### 9.

Do parallelograms have diagonals that are lines of symmetry? If so, draw and explain. If not, draw and explain.

For problems 10 through 12, find the equation:

of a line

**parallel**to the given line and through the indicated-intercept. of a line

**perpendicular**to the given line and through the indicated-intercept.

### 10.

Equation of a line:

#### a.

Parallel line through point

#### b.

Perpendicular to the line through point

### 11.

Table of a line:

#### a.

Parallel line through point

#### b.

Perpendicular to the line through point

### 12.

Graph of a line:

#### a.

Parallel line through point

#### b.

Perpendicular to the line through point