Geometry Help

Geometry is about the shape and size of things. It is the study of points, lines, angles, shapes, their relationships, and their properties.

Videos have been included in almost all the following topics to help reinforce your understanding.

Geometry Lessons

Basic Geometry Terms - Points, Lines, Collinear, Line Segments, Midpoints, Rays, Planes, Coplanar, Space
Pairs of Lines - Intersecting Lines, Parallel Lines, Perpendicular Lines, Skew Lines

Angles

Triangles

Types of Triangles - Right, Acute, Obtuse, Equilateral, Equiangular, Isosceles, Scalene. Oblique Triangles
Right, Acute, Obtuse Triangles
Equilateral, Isosceles, Scalene Triangles

Special Right Triangles 3-4-5 Triangles, 5-12-13 Trisnagles, 45°-45°-90° Triangles, 30°-60°-90° Triangles
3-4-5 Triangles,
45°-45°-90° Triangles
30°-60°-90° Triangles

Area of Triangles - Use of the different formulas to calculate the area of triangles, given base and height, given three sides, given side angle side, given equilateral triangle, given triangle drwan on a grid, given three vertices on coordinate plane, given three vertices in 3D space

Pythagorean Theorem - How to use the Pythagorean Theorem, Converse of the Pythagorean Theorem, Worksheets, Pythagorean Theorem Proofs
Pythagorean Triples- Examples of Pythagorean Triples, Families of Pythagorean Triples, Pythagorean Triples and Right Triangles, Solving Problems using the Pythagorean Triples, How to generate Pythagorean Triples
Pythagorean Theorem Word Problems - How to use the Pythagorean Theorem to solve word problems
Converse of the Pythagorean Theorem - Explain how to use the Converse of the Pythagorean Theorem. Proof of the Converse of the Pythagorean Theorem

Congruent Triangles - SSS rule, SAS rule, AAA rule, AAS rule, HL rule for congruent triangles, CPCTC
SSS rule, SAS rule, ASA rule, AAS rule - Explain the rules, How to use two-column proofs to prove triangles congruent
Hypotenuse Leg (HL) - Why HL is sufficient to prove two right triangles congruent and How to use HL postulate in two-column proofs

Similar Triangles - Properties of similar triangles, AA rule, SAS rule, SSS rule, Solving problems with similar triangles

Triangle Inequality - Triangle Inequality Theorem, Angle-Side Relationship

Triangle Sum Theorem - Proof of the Triangle Sum Theorem. How to use the Theorem to solve geometry problems involing triangles
Exterior Angle Theorem - How to use the Exterior Angle Theorem, How to prove the Exterior Angle Theorem

Interior Angles of a Triangle - Properties of Interior Angles, Solve problems involving interior angles
Exterior Angles of a Triangle - Find unknown exterior angles, Proof the sum of exterior angles
Angles of a Triangle - Summary of the properties of angles in a triangle

Law of Sines or Sine Rule - How to use the Law of Sines, Ambiguous case, Proof for the Law of Sines, Applications using the Law of Sines
Law of Cosines or Cosine Rule - How to use the Law of Cosines, Proof for the Law of Cosines, Applications using the Law of Cosines
Solving a Triangle - SAS - Finding Missing Sides/Angles - How to solve triangles using the Law of Sines

Polygons

Polygons - Types of Polygons: simple or complex, convex or concave, equilateral, equiangular, regular or irregular, Naming Polygons
Angles in Polygons - Sum of Angles in a Triangle, Dividing Polygons into Triangles, Formula for the Sum of Interior and Exterior Angles of a Polygon

Quadrilaterals - Parallelogram, Square, Rhombus, Rectangle, Trapezoid, Kite, Trapezium

Area of Polygons - Formulas for the area of Square, Rectangle, Parallelogram, Triangle, Rhombus, Kite, Trapezoid, any Regular Polygon
Area of Squares and Rectangles - Formulas and practise for the area of Square and Rectangle
Area of Parallelograms - Formula for the area of a parallelogram, Derive the formula for the area of a parallelogram, Word problems using parallelograms
Area of Triangles - Use of the different formulas to calculate the area of triangles, given base and height, given three sides, given side angle side, given equilateral triangle, given triangle drwan on a grid, given three vertices on coordinate plane, given three vertices in 3D space
Area of Rhombus - Use of the different formulas to calculate the area of rhombus, given base and height, given lengths of diagonals, given side and angle
Area of Trapezoids - Area of trapezoids, Derive area formula of trapezoids, Solve problems using area of trapezoids
Area of Shaded Region - How to calculate the area of shaded regions

Perimeters of Polygons - Squares, Rectangles, Parallelograms, Triangle, Rhombus, Trapezoids, Word Problems involving perimeters of polygons

Circles

Circles - diameter, chord, radius, arc, semicircle, minor arc, major arc, tangent, secant, circumference, area, sector
Parts of a circle - Diameter, Chord, Radius, Arc, Tangent, Intersecting Circles, Internal and External Tangents
Circumference of circle
Area of circle
Length of Arc in a circle
Area of Sector

Tangent to a Circle
Angles involving Tangents & Circles

Degrees and Radians
Arc Length of Circle in Radians

Circle Theorems

The Arrow Theorem
The Bow Theorem
"90 Degrees in Semicircle" Theorem
Alternate Segment Theorem
Quadrilaterals in a Circle
Angles in a Circle

Angles and Intercepted Arcs

Solid Geometry

Surface Area of a Cube
Surface Area of a Prism
Surface Area of a Cylinder
Surface Area of a Cone
Surface Area of a Sphere
Surface Area of a Pyramid
Surface Area of Solids

Geometry Nets

Geometrical Formulas

Area Formula: rectangle, parallelogram. rhombus, triangle, regular polygon, trapezium, and circle

Surface Area Formula: sphere, closed cylinder, hollow cylinder, cone and pyramid

Volume Formula: solid cylinder, hollow cylinder, prism, cone, pyramid, and sphere

Formulas Derived: Area of Cone, Volume of Cone, Volume of Sphere

Summary of shapes and formulas

Coordinate Geometry and Graphs

Graphing Quadratic Functions
Graphical Solutions of Quadratic Functions

Graphing Cubic Functions
Graphing Exponential Functions
Graphing Reciprocal Functions

Sketching the Graphs of some Functions

Geometric Construction

Construct and Copy Lines
Construct a Perpendicular Bisector
Construct a Perpendicular Line through a Point
Construct Parallel Lines

Construct a 60° Angle by Constructing An Equilateral Triangle
Construct an Angle Bisector
Construct a 30 Degree Angle
Construct a 45 Degree Angle

Construct A Triangle given the Length of its Three Sides (SSS)
Construct A Triangle given One Side and Two Angles
Construct A Triangle given Two Sides and an Angle

Construct a Parallelogram and a Square

Contruct Various Angles & Shapes : 30°, 45 °, 90°, 120°; hexagon, triangle

Locus of a Moving Point

Geometry Transformation

Geometry / Math Tranformations

Translation involves “sliding” the object from one position to another.

Reflection involves “flipping” the object over a line called the line of reflection.

Rotation involves “turning” the object about a point called the center of rotation.

Dilation involves a resizing of the object. It could result in an increase in size (enlargement) or a decrease in size (reduction).

Geometry Proofs (Videos)

Geometry Practice Questions

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