Geometry - Semester - 2

Recommended Grade Level: 9 - 12

Course Credits: 0.5

Course Price: $285.00

Price $285.00

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Course Details:

This course provides an opportunity for students to explore Trigonometry, Analytic Geometry, and Modeling. Topics include properties and solutions for right triangles, Law of Sines and Cosines and their applications; properties and construction of circles and tangents to circles, properties and construction of cyclic quadrilaterals and regular polygons; parallel and perpendicular lines, deriving their slopes and distance between them; surface area, volume, and perimeter of several types of geometric figures; describing and applying geometric measurements for practical purposes; rotating 2D objects, cross-section of 3D geometric figures; concepts of density and solving design problems using geometric concepts. Students perform constructions, measure figures, observe patterns, discuss their findings, write their own definitions, and formulate and prove geometric conjectures.

Note: This course is not designed for ELL (English Language Learners) students. ELL students may enroll in this course ONLY if they have adequate mentor support at their home school and are able to fulfill all course requirements.

Prerequisites:

Geometry - Semester - 1

Syllabus:

Section 1: Trigonometry of triangle

Objectives:

To use geometric mean and find lengths of segments in a right triangle
To determine and use relations in similar right triangles
Apply the converse of Pythagorean Theorem, to determine is a triangle is right, obtuse or acute
To define and use six trigonometric ratios as ratios of sides of a right triangle
To use properties of 45-45-90 degree and 30-60-90 degree triangles to solve problems
To solve right triangles using trigonometric ratios
To use trigonometric ratios and solve problems involving angle of elevation and angle of depression
To find missing angles in a right triangle using inverse trigonometric ratios
Apply the Law of Sines to solve a triangle
Solve word problems requiring the Law of Sines
Be able to determine the number of triangles that exist in the ambiguous case
Apply the Law of Cosines to solve a triangle
Solve word problems requiring the Law of Cosines

Lessons:

Properties of Right Triangle
Trigonometry of Right Triangles
Special Right Triangles
Solving Right Triangles
Law of Sines and its Applications
Law of Cosines and its Applications

Section 2: Circles

Objectives:

To identify segments and lines related to circle
To identify corresponding central and inscribed angles
To distinguish types of tangents to circles and apply their properties
To construct the circumcircle, incircle and excircle of a triangle
To construct tangents to circle, and common tangent to two circles
To explore some special classes of quadrilaterals such as tangential and cyclic quadrilaterals
To determine and construct the locus of set of points that satisfy a given condition
To construct regular polygons inscribed in a circle

Lessons:

Introduction to Radii, Segments, Lines and Chords as Related to Circles
Angles and Arcs Related to Circles
Constructions of an Inscribed and Circumscribed Circles of a Triangle
Tangent to a Circle
Construction of Tangents to a Circle
Cyclic Quadrilaterals
Construction of Locus
Constructions of a Regular Polygons Inscribed in a Circle

Section 3: Analytical geometry in the plane

Objectives:

To derive an equation of a circle
To identify the radius and the center of a circle using the equation
To plot a circle in two-dimensional coordinate system
To find an equation of line and to express it in different forms
To determine whether lines parallel, perpendicular, or neither
To write equations of parallel or perpendicular lines
To be able to find the angle between two lines
To determine the coordinates of a point of division of line segment
To find the perimeter and area of triangle, rectangle, polygon and composite figures

Lessons:

Deriving equation of a circle
Different Forms of Equations of Lines
Slope of Parallel Lines
Slope of Perpendicular Lines
Angle Between Two Lines
Distance of a Point from a Given Line and Division of a Line Segment
Proving Geometric Theorems Algebraically
Perimeter and Area of Triangle, Rectangle, and Polygon using the Distance Formula

Section 4: Geometric measurements and dimensions

Objectives:

To find perimeter and area of polygons
To find perimeter and area of circle
To understand units, square units, and cubic units and how they are related to perimeter, area and volume
To recognize the shapes of prism, cylinder, pyramid, cone and sphere
Understand the meaning the surface area and volume of three-dimensional figure
To determine surface area and volume of prism, cylinder, pyramid, cone and sphere
To state Cavalieri’s Principle and to use it to prove formulas and problems
To choose appropriate formulas to solve real-life volume and surface area problems

Lessons:

Perimeter and Area of Polygon
Circumference and Area of a Circle
Surface Area and Volume of a Prism
Surface Area and Volume of a Pyramid
Surface Area and Volume of a Cylinder
Surface Area and Volume of a Cone
Surface Area and Volume of a Sphere

Section 5: Modeling with geometry

Objectives:

Model geometric, two-dimensional and three-dimensional shapes by real life examples;
To determine volume of prism, cylinder, pyramid, cone and sphere after doubling, tripling, or halving a dimension;
Identify the shapes of two-dimensional cross sections of three-dimensional objects;
Identify three-dimensional objects generated by rotations of two-dimensional objects;
To determine density of a three-dimensional object;
To determine the density of population;
To solve design problems using geometrical methods and knowledge.

Lessons: