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# Unit 5: Geometry

Students will grow their skills of visual perceptibility by exploring the world of visual mathematics,  2-D and 3-D shapes, the coordinate plane, surface area, volume, transformations and congruence.  Students, having mastered the Discovery Method process, are able to apply it in this unit in its full power. #### Theorems Your Student Will Discover:

Fundamentals Of Geometry

How to find angle measures of intersecting lines

How to find angle measures given parallel lines, a transversal and at least one angle measure

Triangles

Triangle Inequality Theorem

Pythagorean Theorem

Sum of the interior angles of a polygon

How to find the measure of an interior angle of a polygon given the other angles

Area And Perimeter

How to find the measure of the perimeter of a polygon

How to find the measure of the circumference of a circle

How to find the area of a rectangle

How to find the area of a triangle

How to find the area of a regular polygon

How to find the area of a circle

Visual Perceptibility

How to draw the net of a 3-D shape

How to name a 3-D shape

Surface Area And Volume

How to find the surface area of a prism

How to find the surface area of a pyramid

How to find the surface area of a cylinder

How to find the volume of a prism

How to find the volume of a pyramid

How to find the volume of a cylinder

How to find the volume of a cone

How to find the volume of a sphere

Coordinate Plane

How to graph a coordinate pair on the coordinate plane

How to find the distance between two coordinate pairs on the coordinate plane

Transformations

How To Translate A Figure On The Coordinate Plane

How To Reflect A Figure Across The X-Axis

How To Reflect A Figure Across The Y-Axis

How to rotate a shape on the coordinate plane 90 degrees clockwise

How to rotate a shape on the coordinate plane 90 degrees counter-clockwise

How to rotate a shape on the coordinate plane 180 degrees

How to dilate a shape given the scale factor

How to find the scale factor given images of a dilation

#### Definitions:

2-Dimensional

Point

Line

Line Segment

Ray

Angle

Degree

Vertex

Side

Acute Angle

Obtuse Angle

Right Angle

Interior

Exterior

Parallel Lines

Perpendicular Lines

Transversal Line

Congruent

Supplementary Angles

Complementary Angles

Vertical Angles

Triangle

Acute Triangle

Obtuse Triangle

Right Triangle

Equilateral Triangle

Isosceles Triangle

Scalene Triangle

Polygon

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Dodecagon

Regular Polygon

Irregular Polygon

Square

Rhombus

Parallelogram

Trapezoid

Kite

Convex

Concave

Circle

Diameter

Center Of A Circle

Perimeter

Circumference

Area

3-Dimensional

Net

Edge

Face

Pyramid

Prism

Cone

Cylinder

Sphere

Surface Area

Volume

X-Axis

Y-Axis

Origin

Coordinate Plane

Coordinate Pair

Transformation

Congruent

Similar

Translation

Reflection

Symmetry

Line Of Symmetry

Rotation

Clockwise

Counter-Clockwise

Dilation

Scale Factor 