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

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Page 1: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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

Geometry

Page 2: 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.

Page 3: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Transformations

• Reflection

• Rotation

• Translation

Page 4: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Two-Dimensional Figures

Page 5: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Polygons

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

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

Page 6: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Regular Polygons

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

Page 7: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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.

Page 8: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

TrianglesClassified by their sides

•Equilateral Triangle

-all 3 sides equal in length

-all 3 angles equal in measure

Page 9: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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

Page 10: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

TrianglesClassified by their sides

•Scalene Triangle

-0 sides equal in length

Page 11: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

TrianglesClassified by their angles

•Acute Triangle

-all 3 angles acute

60°

60° 60°

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

Page 12: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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°

Page 13: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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°.

Page 14: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Quadrilaterals• A polygon with

4 sides.• Some special

quadrilaterals include:

• Square• Rectangle• Parallelogram• Rhombus• Trapezoid

Page 15: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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°

Page 16: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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°

Page 17: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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°

Page 18: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Parallelogram

•Opposite sides parallel

•The sum of the angles equals 360°.

80°+ 80° + 100° + 100° = 360°

80°

80° 100°

100°

Page 19: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Trapezoid

•Has one pair of parallel sides

•The sum of the angles equal 360°.

80°+ 80° + 100° + 100° = 360°

100°100°

80°80°

Page 20: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

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

Page 21: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Find the missing angle measurement in the

quadrilateral.

80°

100° 100°

1 = ____ 80°

1

Page 22: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Find the missing angle measurement in the triangle.

90°

60° 1 = ____ 30°

1

Page 23: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Find the missing angle measurement in the

quadrilateral.

90°

90° 80° 1 = ____ 100°

1

Page 24: The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Geometry

Find the missing angle measurement in the triangle.

78° 78°

1 1 = ____ 24°