Geometry Help



Geometry Topics


Angles


Triangles


Polygons


Circles


Circle Theorems


Solid Geometry



Geometric Formulas


Coordinate Geometry & Graphs


Geometric Constructions


Transformations


Geometric Proofs


Practice Questions


Looking for some Geometry Help? Our materials here review the basic terms and concepts in geometry and provide further lessons to help you develop your understanding of geometry and its applications to solving problems in real life. 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.

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

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

Triangles

Types of Triangles Right, Acute, Obtuse, Equilateral, Equiangular, Isosceles, Scalene. Oblique Triangles
Special Right Triangles 3-4-5 Triangles, 5-12-13 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 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 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

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

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, Two-Tangent 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



Circle Theorems

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.


Solid Geometry

Volume and Surface Area of Solids Volume and surface area of cubes, cuboids, prisms, cylinders, spheres, cones, pyramids



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


Geometric Formulas

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 and Graphs

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, y-intercept
Equation of a LineThe slope-intercept form for the equation of a line, how to write equations in slope-intercept 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 slope-intercept form, the point-slope 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 x-intercept and y-intercept, how to graph linear equations using the slope and y-intercept.
Slope and Intercept of a Linear EquationHow to graph a linear equation when the equation is given in slope-intercept 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 y-intercept 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 = ax2, the properties of the graph y = ax2, 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(xh)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 = axn c, how to sketch some basic or common graphs.





Geometric Constructions

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.

Geometric Transformations

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).

Geometric Proofs (Videos)

Triangle Medians and Centroids (2D Proof)
Area Circumradius Formula Proof
Proof that the diagonals of a rhombus are perpendicular bisectors of each other


Geometry Practice Questions

Free SAT Practice Questions (with Hints & Solutions) - Geometry




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