The mathematical study of the properties, measurements, and relationships of points, lines, planes,...

The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids.

Geometry

Lines of Symmetry

• A line that divides a figure into two halves that are reflections of each other.

Transformations

• Reflection

• Rotation

• Translation

Two-Dimensional Figures

Polygons

•A simple closed figure formed by 3 or more sides.

•The number of sides determines the name of the polygon.

Regular Polygons

•A regular polygon is a polygon with all sides congruent and all angles congruent.

Triangles

•A polygon with 3 sides and 3 angles.

•Triangles can be classified by the length of their sides.

•Triangles can be classified by the kind of angles.

TrianglesClassified by their sides

•Equilateral Triangle

-all 3 sides equal in length

-all 3 angles equal in measure

TrianglesClassified by their sides

•Isosceles Triangle

-2 sides are congruent

-the two angles opposite the congruent sides, angles K and L, are the base angles

-the base angles are congruent

K L

M

TrianglesClassified by their sides

•Scalene Triangle

-0 sides equal in length

TrianglesClassified by their angles

•Acute Triangle

-all 3 angles acute

60°

60° 60°

The sum of the angles in a triangle equals 180°.

TrianglesClassified by their angles

•Obtuse Triangle

-1 obtuse angle

-2 acute angles

The sum of the angles in a triangle equals 180°.

120° 35°

25°

TrianglesClassified by their angles

•Right Triangle

-1 right (90°) angle

-2 acute angles

90°

60°

30°

The sum of the angles in a triangle equals 180°.

Quadrilaterals• A polygon with

4 sides.• Some special

quadrilaterals include:

• Square• Rectangle• Parallelogram• Rhombus• Trapezoid

Square

• 4 right (90°) angles

• Opposite sides parallel

• All sides equal in length

90°90°

90° 90°

• The sum of the angles equals 360°.

90°+ 90° + 90° + 90° = 360°

90° x 4 = 360°

Rectangle

• 4 right (90°) angles

• Opposite sides parallel

• Opposite sides equal in length

90°90°

90° 90°

• The sum of the angles equals 360°.

90°+ 90° + 90° + 90° = 360°

90° x 4 = 360°

Rhombus

• Opposite sides parallel

• All sides equal in length

• The sum of the angles equals 360°.

80°+ 80° + 100° + 100° = 360°

80°

80° 100°

100°

Parallelogram

•Opposite sides parallel

•The sum of the angles equals 360°.

80°+ 80° + 100° + 100° = 360°

80°

80° 100°

100°

Trapezoid

•Has one pair of parallel sides

•The sum of the angles equal 360°.

80°+ 80° + 100° + 100° = 360°

100°100°

80°80°

Compare a rectangle and a parallelogram.

Are alike because:• opposite sides

parallel• opposite sides congruent

• four sides

Are different because:• rectangles have

four right angles

Find the missing angle measurement in the

quadrilateral.

80°

100° 100°

1 = ____ 80°

1

Find the missing angle measurement in the triangle.

90°

60° 1 = ____ 30°

1

Find the missing angle measurement in the

quadrilateral.

90°

90° 80° 1 = ____ 100°

1

Find the missing angle measurement in the triangle.

78° 78°

1 1 = ____ 24°