  Red Comet  ## Geometry - Semester - 2

#### Course Price: \$250.00  ## 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.

## 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
• 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:

• Application of the Volumes of Cones, Cylinders, Pyramids and Spheres
• Rotating 2D Objects
• Cross-Sections of Three-Dimensional Objects
• Describing an Object Using Geometrical Concepts
• Applying Concepts of Density in Modeling Situations
• Solving Design Problems Using Geometrical Methods

### Accreditation & Approvals          