# 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

Quadrilaterals

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*

*Adjacent 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*

*Quadrilateral*

*Parallelogram*

*Trapezoid*

*Kite*

*Convex*

*Concave*

*Circle*

*Radius*

*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*

*Quadrant*

*Coordinate Pair*

*Transformation*

*Congruent*

*Similar*

*Translation*

*Reflection*

*Symmetry*

*Line Of Symmetry*

*Rotation*

*Clockwise*

*Counter-Clockwise*

*Dilation*

*Scale Factor*

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