# 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.

### 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
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
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

### 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.
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 Cube
How 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 Cuboid
How to calculate the surface area of a cuboid, how to solve word problems about cuboids, nets of a cuboid.
Surface Area of a Prism
Calculate 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 Cylinder
Calculate 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 Cone
Calculate 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 Sphere
Calculate 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.

### 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).

### Geometry Practice Questions

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

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