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Geometry Help


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.



Geometry Topics


Angles


Triangles


Polygons


Circles


Circle Theorems


Solid Geometry


Geometric Formulas


Coordinate Geometry & Graphs


Geometric Constructions


Transformations


Geometric Proofs


Practice Questions

Examples, solutions, and videos have been included in almost all the following topics to help reinforce your understanding.

Introduction to Geometry

Angles




Triangles



Polygons

  • Introduction to 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
    Polygons Describe the characteristics of a polygon
  • Area & Perimeter of Polygons
    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

  • Parts of a Circle
    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
  • Area & Circumference of Circle
    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.
  • Degrees & Radians
    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
    Area of Sector Area of a sector formula in degrees and radians, area of segment

Circle Theorems

  • Chords & Intercepted Arcs
    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.
  • Angles in 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 Inscribed angles subtended by the same arc or chord are equal.
    Thales' Theorem Triangle inscribed in semicircle or Angle inscribed in semicircle or ӹ0 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 of Solids
    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.
    Volume & Surface Area of Solids Volume and surface area of cubes, cuboids, prisms, cylinders, spheres, cones, pyramids
  • Surface Area of Solids
    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, Surface Area, Volume 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 Plane
    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
  • Midpoint & Distance Formulas
    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.
  • Graph Quadratic Functions
    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.
  • Cubic & Reciprocal Functions
    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

  • Locus of Points
    Locus of a Moving Point The rules of the Locus Theorem, 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

  • Types of 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

Geometry Practice Questions

Free SAT Practice Questions (with Hints & Solutions) - Geometry
Graphing Calculator with step by step solutions
Step By Step Graphing
Points, Lines, and Line Segments
Linear Equations and Functions
Conic Sections
Polar Equations

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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