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Geometry

Guiding Principle

A student at the proficient level in Geometry will be able to demonstrate understanding of high school mathematics by solving problems, reasoning, communicating, representing, and making connections based on the following indicators:

Benchmark/Topics

As a result of studying Geometry, I will be able to:

(1) Lines and Angles

· Midpoints

· Distance formula

· Parallel

· Perpendicular

4.0.1 Demonstrate an understanding of basic geometric relationships when I can

· Identify a midpoint

o Apply the midpoint formula

o Apply the distance formula

o Determine relationships of parallel lines

o Determine relationships of perpendicular lines

(2) Logical Reasoning

· Conditionals

· Indirect Proof

· Formal Two Column Proof

4.0.2 Apply logical reasoning to

o Interpret conditional statements

o Justify conditional statements using indirect proof

o Justify conditional statements using formal two column proof

(3) Congruent Polygons

· Definition

· Proof

4.2.3 Demonstrate an understanding of the properties of congruent polygons when I can

o Classify congruent polygons by definition

o Show two polygons are congruent using formal proof

(4) Similar Polygons

· Triangle Properties

· Ratio/Proportion

5.1.4 Demonstrate knowledge of similar polygons when I can

o Identify the properties of similar triangles

o Apply properties of ratio and proportion to solve problems involving indirect measurement

(5) Quadrilaterals

· Parallelograms

· Trapezoids

· Squares

· Rectangles

· Rhombus

4.2.5 Identify, state the properties and determine the relationships between each of the following quadrilaterals:

o Parallelograms

o Trapezoids

o Squares

o Rectangles

o Rhombi

(6) Right Triangle Trig

· Geometric Mean

· Pythagorean Theorem

· Special Right Triangles

· Sine, Cosine, Tangent

4.5.6 Apply right triangle properties to problem situations when I can

o Solve geometric mean problems

o Apply the Pythagorean Theorem

o State the properties of special right triangles

o 30-60-90 triangle

o 45-45-90 triangle

o Apply the sine, cosine and tangent ratios

(7) Circles

· Circumference

· Area

· Secants

· Tangents

· Chords

4.0.7 Demonstrate an understanding of circles and their properties when I can

o Calculate the circumference

o Determine the area

o Define special cases of segments and lines related to circles and develop and use theorems about measures of the following

o Secants

o Tangents

o Chords

(8) Area and Volume

4.1.8 define and use the appropriate formula for

o Finding the area of

o Triangles

o Quadrilaterals

o Regular Polygons

o Circles

o Finding the volume and surface area of

o Right rectangular prisms

o Right circular prisms

o Right rectangular pyramids

o Right cones

(9) Coordinate Geometry

4.3.9 Use coordinate geometry to

o Solve problems on the coordinate plane

o Confirm theorems using coordinate proof

(10) Constructions

4.0.10 Perform the following constructions:

o Copy a given segment

o Copy a given angle

o Perpendicular bisector of a segment

o Perpendicular through a point not on a given line

o Perpendicular through a point on a given line

o Angle bisector

o Parallel line through a point not on a given line

(11) Normal Distributions

· 68-95-99.7 Rule

· Data

6.6.11 Describe the normal curve and use its properties when I can

o Apply the 68-95-99.7 rule

o Answer questions about sets of data that are assumed to be normally distributed

*Benchmark Key – State Content Standard . State Benchmark . District Benchmark