Geometry Topics 

Videos have been included in almost all the
following topics to help reinforce your understanding.
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
How to Name an Angle. Angles Around a Point

Measuring Angles How to use a
protractor to measure an angle

Drawing Angles How to use a
protractor to draw different types of angles

Types of Angles Right Angles,
Acute Angles, Obtuse Angles, Straight Angles, Reflex
Angles and Full Angles

Pairs of Angles Complementary,
Supplementary, Vertical, Corresponding, Alternate
Interior, Alternate Exterior and Adjacent Angles

Complementary &
Supplementary Angles Solve problems using
Complementary and Supplementary Angles

Vertical Angles
Solving problems using Vertical Angles, Proof of the
Vertical Angle Theorem

Corresponding Angles
Corresponding Angle Theorem, Converse of the Corresponding
Angle Postulate

Alternate Interior
& Exterior Angles Alternate Interior Angle and
Alternate Exterior Angle Theorems, Proofs and Converse

"Find the angle" problems
Summary of all the different angle properties and how they
can be used to find missing angles

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


Special Right Triangles 345
Triangles, 51213 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 drawn 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
twocolumn 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 twocolumn proofs

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

Triangle Inequality Triangle
Inequality Theorem, AngleSide Relationship

Triangle Sum Theorem Proof of the
Triangle Sum Theorem. How to use the Theorem to solve
geometry problems involving 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 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 practice 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 drawn 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 involving polygons
and circles.

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

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 Find pi, Formula for circumference of circle,
Find circumference, Find radius, diameter and area when
given circumference

Arc of a Circle Arc of a circle,
Central Angle, Arc Measure, Arc Length Formulas for arc
measure given in degrees or in radians.

Area of circleFormula
for area of circle, Find area, Find radius, diameter and
circumference when given area

Area of Sector Area of a sector
formula in degrees and radians, area of segment

Area of Shaded Region How to
calculate the area of shaded regions involving polygons
and circles.

Tangent to a Circle Point of
Tangency, Tangent to a Circle Theorem, Secant, TwoTangent
Theorem, Common Internal and External Tangents

Angles, Tangents & Circles
Find angles involving Tangents and Circles

Degrees and Radians Measure
angles in degrees, minutes and seconds, Convert to decimal
notation, Add and subtract angles, Measure angles in
radians, Convert between degrees and radians

Arc Length of Circle in Radians
Formula for arc length when arc measure is in radians,
Solving problems using arc length formula

Chords of a Circle Perpendicular
bisector of a chord passes through the center of a circle,
Congruent chords are equidistant from the center of a
circle, If two chords in a circle are congruent, then
their intercepted arcs are congruent, If two chords in a
circle are congruent, then they determine two central
angles that are congruent.

Angles and Intercepted Arcs
Formulas relating the angles and the intercepted arcs of
circles.
Measure of a central angle. Measure of an inscribed angle (angle with its vertex on the circle) Measure of an angle with vertex inside a circle. Measure of an angle with vertex outside a circle. 
The Inscribed Angle Theorem Inscribed angles and central angles, The
Inscribed Angle Theorem or The Central Angle Theorem or
The Arrow Theorem.

The Bow Theorem
Inscibed angles subtended by the same arc or chord are
equal.

Thales' Theorem Triangle inscribed in semicircle or
Angle inscribed in semicircle or 90 degrees in
Semicircle Theorem or Thales' Theorem

Alternate Segment
Theorem An angle between a tangent and a chord
through the point of contact is equal to the angle in the
alternate segment.

Quadrilaterals in a Circle
Cyclic Quadrilateral, the opposite angles of a cyclic
quadrilateral are supplementary, the exterior angle of a
cyclic quadrilateral is equal to the interior opposite
angle.

Angles in a Circle A review and
summary of the properties of angles that can be formed in
a circle and their theorems.

Volume of Cubes What is volume, how to find the volume of a cube, how
to solve word problems about cubes, nets of a cube.

Volume of Rectangular
Prisms How to find the volume
of a rectangular prism, how to solve word
problems about rectangular prisms

Volume of Prisms What
is a prism, how to find the
volume of prisms, how to solve word problems
about prisms.

Volume of Cylinders How
to find the volume of cylinders, how
to find the volume of hollow cylinders or tubes, how
to solve problems about cylinders.

Volume of Spheres How
to find the volume of a sphere, how to find the
volume of a hemisphere, how to prove the formula for the
volume of a sphere.

Volume of Cones What is a cone, how to calculate the volume of a cone, how
to solve word problems about cones, how to prove the
formula of the volume of a cone.

Volume of Pyramids What is a
pyramid, how to find the volume of a pyramid, how to solve
word problems about pyramids, the relationship between the
volume of a pyramid and the volume of a prism with the
same base and height.

Surface Area of a CubeHow to
calculate the surface area of a cube, how to find the
length of a cube given the surface area, nets of a cube.

Surface Area of a CuboidHow to
calculate the surface area of a cuboid, how to solve word
problems about cuboids, nets of a cuboid.

Surface Area of a PrismCalculate
the surface area of prisms: rectangular prisms,
triangular prisms, trapezoidal prisms, hexagonal prisms
etc., solve problems about prisms. calculate the
surface area of prisms using nets.

Surface Area of a CylinderCalculate the surface area of solid
cylinders, calculate the
surface area of hollow cylinders, solve word
problems about cylinders, calculate the surface area of
cylinders using nets.

Surface Area of a ConeCalculate
the surface area of a cone when given the slant height,
calculate the surface area of
a cone when not given the slant height, solve
word problems about cones, derive the formula for the
surface area of a cone

Surface Area of a SphereCalculate
the surface area of a sphere, calculate the
surface area of a hemisphere, solve problems about surface
area of spheres, prove the formula of the surface area of
a sphere.

Surface Area of a Pyramid Find
the surface area of any pyramid, find the surface area of
a regular pyramid, find the surface area of a square
pyramid, find the surface area of a pyramid when the slant
height is not given.

Geometric Nets Nets of solids:
cubes, cuboids, triangular prisms, prisms, pyramids,
cylinders, cones.

Surface Area of Solids Using nets
to calculate the surface area of solids: cube, rectangular
prism or cuboid, triangular prism, cylinder, and pyramids

Area Formula: Gives the area
formula for square, rectangle, parallelogram. rhombus,
triangle, regular polygon, trapezoid (trapezium), circle
and ellipse.

Surface Area Formula: Gives
the surface area formula for cube, cuboid, prism, solid
cylinder, hollow cylinder, cone, pyramid, sphere and
hemisphere

Volume Formula: Gives the volume
formula for cube, cuboid, prism, solid cylinder, hollow
cylinder, cone, pyramid, sphere and hemisphere

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

Summary of shapes and formulas Describes the common geometrical shapes
and the formulas to calculate their area and perimeter.
It also includes the use of the Pythagorean Theorem and
Heron's formula.


Coordinate Geometry
Coordinate plane, Slope Formula, Equation of a Line,
Slopes of parallel lines, Slope of perpendicular lines,
Midpoint Formula, Distance Formula

Coordinate PlaneThe coordinate
plane or Cartesian plane, points on the Cartesian Plane,
quadrants

Slope of a Line Slope of line
from the graph (rise over run), using the slope formula,
negative slope, yintercept

Equation of a LineThe slopeintercept
form for the equation of a line, how to write
equations in slopeintercept form, how to write equations
of horizontal and vertical lines, how to get the equation
of a line given two points on the line.

Forms of Linear
EquationsThe slopeintercept form, the pointslope
form, the general form, the standard form, how to convert
between the different forms of linear equations.

Graphing Linear
EquationsHow to graph linear equations by plotting
points, how to graph linear equations by finding the xintercept
and yintercept, how to graph linear equations
using the slope and yintercept.

Slope and Intercept
of a Linear EquationHow to graph a linear equation
when the equation is given in slopeintercept form or when
the equation is given in general form.

Explore the straight line graph
Activity to investigate how the change of the slope and yintercept
can affect the straight line graph.

Slopes of Parallel and Perpendicular
LinesHow to determine if two lines are parallel or
perpendicular when given their slopes, how to find the
equation of a line given a point on the line and a line
that is parallel or perpendicular to it, how to find
parallel or perpendicular lines using Standard Form.


Midpoint FormulaThe midpoint
formula, how to find the midpoint given two endpoints, how
to find one endpoint given the midpoint and another
endpoint, how to proof the midpoint formula.

Distance FormulaHow to derive the
distance formula from the Pythagorean Theorem, how to use
the distance formula.

Graphing Linear
Inequalities Graph of linear inequalities, how to
graph linear inequalities, how to graph systems of linear
inequalities.


Linear Programming
Linear programming, how to use linear programming to solve
word problems.

Quadratic Functions
The different forms of quadratic functions, general form,
factored form, vertex form, convert from general form to
factored form, convert from the general form to the vertex
form using the vertex formula, convert from the general
form to the vertex form using completing the square.

Graphing Quadratic Functions
How to graph of quadratic functions by plotting points,
how to graph quadratic function of the form y =
ax^{2, }the properties of the graph y
= ax^{2}, how to graph a quadratic
function given in general form, how to graph a quadratic
function given in factored form, how to graph a quadratic
function given in vertex form.

Graphical Solutions of Quadratic
Equations How the solutions of a quadratic
equation is related to the graph of the quadratic
function, how to use the graphical method to solve
quadratic equations.

Graphing Cubic Functions How to
graph of cubic functions by plotting points, how to graph
cubic functions of the form y = a(x
− h)^{3} + k.

Graphing Exponential Functions
How to graph exponential functions by plotting points, the
characteristics of exponential functions, how to use
transformations to graph an exponential function.

Graphing Reciprocal Functions
How to graph reciprocal functions by plotting points, the
characteristics of graphs of reciprocal functions, how to
use transformations to graph a reciprocal function, how to
get the equation of a reciprocal function when given its
graph.

Sketching the Graphs of some
Functions How to graph functions of the form y = ax^{n} + c,
how to sketch some basic or common graphs.

Construct a Perpendicular Line
through a Point How to construct a perpendicular
to a line through a point on a line. how to construct a
perpendicular to a line through a point not on a line.


Construct Parallel
Lines How to construct parallel lines, how to
construct a line parallel to another line and through a
given point.


Construct an Angle Bisector How
to construct an angle bisector of a given angle, how to
use an angle bisector to construct some angles for
example, 90 degrees, 45 degrees, 60 degrees, 30 degrees,
120 degrees, 135 degrees. 15 degrees.


Construct A Triangle Given the
Length of its Three Sides (SSS)


Construct A Triangle Given One
Side and Two Angles (ASA)

Construct A Triangle Given Two
Sides and an Angle (SAS)

Construct
Parallelogram, Square & Rectangle How to
construct a parallelogram given the lengths of its sides
and an angle, how to construct a parallelogram given the
lengths of its diagonals, how to construct a square given
the length of the diagonal, how to construct a square
given the length of one side.

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

Locus of a Moving Point The
rules of the Locus Theroem, how the rules of the Locus
Theorem can be used in real world examples, how to
determine the locus of points that will satisfy more than
one condition.

Geometry / Math Transformations
Translation, Reflection, Rotation, Dilation or Enlargement

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).

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