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Geometry
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Virtual Nerd tutorials in Geometry, organized by topic.
Geometry
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Fundamentals of Geometry
Points, Lines, and Planes
What is a Plane?
What is a Point?
Measuring Segments
What are the Customary Units of Length?
What are the Endpoints of a Line Segment?
What are the Metric Units of Length?
What Does Congruent Mean?
What is a Line Segment?
Measuring Angles
How Do You Find Angle Measures Using the Angle Addition Postulate?
What are Acute, Obtuse, Right, and Straight Angles?
What Does Congruent Mean?
What is a Degree?
What is a Ray?
What is an Angle?
Angle Pair Relationships
What are Complementary Angles?
What are Perpendicular Lines?
What are Supplementary Angles?
What are Vertical Angles?
Distance and Midpoints
How Do You Bisect a Segment by Constructing?
How Do You Find the Distance Between Two Points?
How Do You Find the Midpoint Between Two Coordinates?
How Do You Find the Midpoint of Two Points on a Map If You Have the Coordinates?
How Was the Distance Formula Derived?
What Is the Distance Formula?
What's the Midpoint Formula?
What's the Midpoint of Two Points on a Number Line?
Perimeter, Circumference, and Area
How Do You Find the Area of a Circle if You Know the Diameter?
How Do You Find the Area of a Circle if You Know the Radius?
How Do You Find the Area of a Rectangle?
How Do You Find the Area of a Triangle?
How Do You Find the Circumference of a Circle if You Know the Diameter?
How Do You Find the Circumference of a Circle if You Know the Radius?
How Do You Find the Perimeter of a Rectangle?
How Do You Find the Perimeter of a Shape?
What is Area?
What is Circumference?
What is the Formula for the Area of a Circle?
What is the Formula for the Area of a Rectangle?
What is the Formula for the Area of a Triangle?
What's the Formula for the Perimeter of a Rectangle?
Reasoning and Proof
Inductive Reasoning
What is Inductive Reasoning?
Conditional and Biconditional Statements
How Do You Write a Biconditional Statement?
How Do You Write the Converse, Inverse, and Contrapositive of a Conditional Statement and Determine Their Truth Values?
What is a Biconditional Statement?
Deductive Reasoning
How Do You Use the Law of Detachment to Draw a Valid Conclusion?
What is the Law of Syllogism?
Geometric and Algebraic Proof
What is a Theorem?
Logic
What's a Venn Diagram, and How Do You Find the Intersection and Union of a Set?
Parallel and Perpendicular Lines
Parallel Lines and Transversals
How Do You Find Missing Angles in a Transversal Diagram?
What are Parallel Lines?
What are Skew Lines?
What is the Corresponding Angles Postulate?
Slopes of Lines
How Do You Find the Slope of a Line from a Graph?
How Do You Find the Slope of a Line from Two Points?
How Do You Know if Two Lines are Parallel?
How Do You Know if Two Lines are Perpendicular?
What Does 0 Slope Mean?
What Does Negative Slope Mean?
What Does Positive Slope Mean?
What Does the Slope of a Line Mean?
What Does Undefined Slope Mean?
What is Rate of Change?
What's the Formula for Slope?
Lines In the Coordinate Plane
How Do You Graph a Horizontal Line?
How Do You Graph a Line If You're Given the Slope and the Intercept?
How Do You Graph a Vertical Line?
How Do You Put an Equation in Point-Slope Form Into Standard or Slope-Intercept Form?
How Do You Put an Equation in Standard Form Into Slope-Intercept or Point-Slope Form?
How Do You Write an Equation for a Horizontal Line?
How Do You Write an Equation for a Vertical Line?
How Do You Write an Equation of a Line in Point-Slope Form If You Have the Slope and One Point?
How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
How Do You Write an Equation of a Line in Slope-Intercept Form If You Have One Point and a Parallel Line?
How Do You Write an Equation of a Line in Slope-Intercept Form If You Have One Point and a Perpendicular Line?
How Do You Write the Equation of a Line in Slope-Intercept Form If You Have the Slope and the Y-Intercept?
How Do You Write the Equation of a Line in Slope-Intercept Form If You Have Two Points?
What's Point-Slope Form of a Linear Equation?
What's Slope-Intercept Form of a Linear Equation?
Proving Lines Parallel
How Do You Find a Value for x that Makes Two Lines Parallel?
What is the Converse of the Corresponding Angles Postulate?
Parallel and Perpendicular Lines
How Do You Construct a Line Parallel to Another Line Through a Given Point?
How Do You Construct a Line Perpendicular to Another Line Through a Given Point On the Line?
How Do You Use Parallel and Perpendicular Theorems to Prove a Relationship Between Two Lines?
Congruent Triangles
Introduction to Triangles
How Do You Classify Triangles?
What are Acute, Obtuse, and Right Triangles?
What are Equilateral, Isosceles, and Scalene Triangles?
What is a Triangle?
Angles in Triangles
How Do You Find a Missing Angle in a Right Triangle?
How Do You Find a Missing Angle in a Triangle?
How Do You Find Missing Angles in a Triangle With Variables?
What are Interior and Exterior Angles of a Polygon?
What is the Triangle Sum Theorem?
Congruence in Triangles
How Do You Identify Corresponding Parts in Congruent Triangles?
What Does Congruent Mean?
Proving Triangles Congruent by SSS and SAS
How Do You Determine if Triangles on the Coordinate Plane are Congruent?
What is the Side-Angle-Side Postulate for Triangle Congruence?
Proving Triangles Congruent by ASA, AAS, and HL
How Do You Show that Corresponding Parts of Congruent Triangles are Congruent?
How Do You Use a Congruence Postulate to Prove Triangles are Congruent?
What is CPCTC?
What is the Angle-Side-Angle Postulate for Triangle Congruence?
Isosceles and Equilateral Triangles
How Do You Construct an Equilateral Triangle?
How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
How Do You Find Missing Angles in an Isosceles Triangle?
Why Are the Angles of Equilateral Triangles Always Equal to 60°?
Congruence in Right Triangles and Overlapping Triangles
How Do You Identify Common Parts in Overlapping Triangles?
How Do You Prove that Two Overlapping Triangles are Congruent?
What are the Legs and Hypotenuse of a Right Triangle?
What is the Hypotenuse-Leg Congruence Theorem?
Relationships Within Triangles
Perpendicular and Angle Bisectors
How Can You Tell if a Point is on the Perpendicular Bisector of a Line Segment?
How Do You Construct a Perpendicular Bisector?
What is a Perpendicular Bisector?
What is the Circumcenter of a Triangle?
What is the Incenter of a Triangle?
Medians and Altitudes of Triangles
How Do You Use the Centroid to Find Segment Lengths in a Triangle?
What is a Median of a Triangle?
Midsegments of Triangles
What is the Triangle Midsegment Theorem?
Inequalities in One Triangle
How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?
How Do You Put the Sides of a Triangle in Order According to Size if You Know Two Angles of the Triangle?
What's the Addition Property of Inequality?
What's the Subtraction Property of Inequality?
Inequalities in Two Triangles
How Do You Use the Hinge Theorem to Compare Side Lengths in Two Triangles?
What is the Hinge Theorem?
Indirect Proof
How Do You Write an Indirect Proof?
Quadrilaterals
Polygons
How Do You Find a Missing Angle in a Quadrilateral?
How Do You Find Measures of Missing Exterior Angles?
How Do You Find Missing Angles in a Quadrilateral With Variables?
How Do You Find the Sum of the Interior Angles of a Polygon?
What is a Polygon?
What is a Regular Polygon?
Properties of Parallelograms
What is a Parallelogram?
What is a Quadrilateral?
Showing a Quadrilateral is a Parallelogram
How Do You Find Values for Variables in the Angles of a Quadrilateral To Make it a Parallelogram?
Special Parallelograms: Rectangles, Rhombuses, and Squares
How Do You Classify Quadrilaterals?
How Do You Construct a Square?
How Do You Find the Value for a Variable in the Angles of a Quadrilateral To Make it a Rhombus?
How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?
What is a Rectangle?
What is a Rhombus?
What is a Square?
Trapezoids and Kites
What is a Trapezoid?
Coordinate Proof
How Do You Use Variables to Name Coordinates for a Figure Placed on the Coordinate Plane?
How Do You Write a Coordinate Proof?
Similarity
Ratios and Proportions
How Do You Find the Angles in a Triangle if You Have a Ratio of Their Measures?
How Do You Find the Scale of a Model?
How Do You Solve a Proportion Using Cross Products?
How Do You Solve a Scale Model Problem Using a Proportion?
How Do You Solve a Scale Model Problem Using a Scale Factor?
How Do You Use the Scale on a Map to Find an Actual Distance?
How Do You Write a Ratio From a Word Problem?
What are the Means and Extremes of Proportions?
What is a Scale Drawing?
What is a Scale?
What's a Proportion?
What's a Ratio?
What's the Means-Extremes Property of Proportions?
Similar Polygons
How Do You Find a Scale Factor in Similar Figures?
How Do You Find Missing Measurements of Similar Figures Using a Proportion?
What are Corresponding Parts in Similar Figures?
What are Similar Figures?
Similar Triangles
How Do You Solve a Problem Using Indirect Measurement with Shadows?
Parallel Lines and Proportional Parts
How Do You Use the Triangle Proportionality Theorem to Find Missing Lengths in a Diagram?
Dilations and Similarity Transformations
What is a Dilation?
Right Triangles and Trigonometry
The Pythagorean Theorem and its Converse
How Do You Determine if a Triangle Is a Right Triangle if You Know its Sides?
How Do You Find the Length of a Leg of a Right Triangle?
What is the Converse of the Pythagorean Theorem?
What is the Pythagorean Theorem?
Similarity in Right Triangles
How Do You Find a Geometric Mean?
What is a Geometric Mean?
Special Right Triangles
How Do You Find a Missing Hypotenuse in a 45°-45°-90° Triangle?
How Do You Find Missing Sides in a 30°-60°-90° Triangle?
What is a 30-60-90 Degree Triangle?
What is a 45°-45°-90° Triangle?
Trigonometric Ratios
How Do You Find a Missing Side of a Right Triangle Using Cosine?
How Do You Find a Missing Side of a Right Triangle Using Sine?
How Do You Find a Missing Side of a Right Triangle Using Tangent?
How Do You Find the Cosine of an Angle in a Right Triangle?
How Do You Find the Sine of an Angle in a Right Triangle?
How Do You Find the Tangent of an Angle in a Right Triangle?
What is the Sine Ratio?
What is the Tangent Ratio?
Angles of Elevation and Depression
How Do You Solve a Problem Using an Angle of Elevation?
Vectors
What is a Vector?
Solving Right Triangles
What is the Law of Cosines?
What is the Law of Sines?
Transformations
Translations
How Do You Use Coordinates to Translate a Figure Horizontally?
How Do You Use Coordinates to Translate a Figure Vertically?
What is a Transformation?
What is an Image?
What Properties of a Figure Stay the Same After a Translation?
Reflections
How Do You Use a Graph to Reflect a Figure Over the X-Axis?
How Do You Use a Graph to Reflect a Figure Over the Y-Axis?
How Do You Use Coordinates to Reflect a Figure Over the X-Axis?
How Do You Use Coordinates to Reflect a Figure Over the Y-Axis?
Rotations
How Do You Rotate a Figure 180 Degrees Around the Origin?
Compositions of Transformations
How Do You Graph a Glide Reflection?
Symmetry
What is Rotational Symmetry?
Dilations
How Do You Make a Figure Larger Using a Dilation?
Similarity and Congruence Transformations
How Do You Identify a Congruence Transformation?
How Do You Identify a Similarity Transformation?
What is a Congruence Transformation, or Isometry?
Circles
Circles and Tangent Lines
How Do You Determine Whether a Line is Tangent to a Circle?
How Do You Find the Diameter of a Circle if You Know its Radius?
What is a Circle?
What is a Tangent Line to a Circle?
Arcs and Chords
How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
Inscribed Angles
How Do You Find Missing Measures of Angles in Quadrilaterals Inscribed in Circles?
How Do You Find The Measure of an Inscribed Angle When You Know the Measure of the Intercepted Arc?
What is a Sector and Central Angle?
Angle Measures and Segment Lengths
How Do You Find the Measure of an Angle Created by Intersecting Chords in a Circle?
How Do You Use Intersecting Chords to Find Arc Measures in a Circle?
Circles in the Coordinate Plane
What is a Circle?
Length and Area
Areas of Parallelograms and Triangles
How Do You Find the Area of a Parallelogram?
How Do You Find the Area of a Triangle?
How Do You Find the Height of a Triangle if You Know the Area and Base?
What is the Formula for the Area of a Parallelogram?
What is the Formula for the Area of a Triangle Using Sines?
What is the Formula for the Area of a Triangle?
Areas of Trapezoids, Rhombuses, and Kites
How Do You Find the Area of a Trapezoid?
How Do You Find the Height of a Trapezoid if You Know the Area and Bases?
What is the Formula for the Area of a Trapezoid?
Circumference and Arc Length
How Do You Find the Circumference of a Circle if You Know the Diameter?
How Do You Find the Circumference of a Circle if You Know the Radius?
How Do You Find the Radius of a Circle if You Know the Circumference?
What is Circumference?
Areas of Circles and Sectors
How Do You Find the Area of a Circle if You Know the Diameter?
How Do You Find the Area of a Circle if You Know the Radius?
How Do You Find the Area of a Sector of a Circle?
How Do You Find the Radius of a Circle if You Know the Area?
What is the Formula for the Area of a Circle?
What is the Formula for the Area of a Sector of a Circle?
Areas of Regular Polygons and Composite Figures
How Do You Find the Area of a Composite Figure?
How Do You Find the Area of a Regular Polygon When You Know the Length of the Apothem?
What is a Composite Figure?
Perimeter and Area of Similar Figures
How Do You Use Similar Figures to Find the Area of a Polygon?
Geometric Probability and Simulations
How Do You Find Geometric Probability Using Areas?
How Do You Use a Simulation to Solve a Problem?
Surface Area and Volume of Solids
Introduction to Solid Geometry
How Do You Identify a Three-Dimensional Figure from a Net?
What is a Cone?
What is a Cylinder?
What is a Net?
What is a Prism?
What is a Pyramid?
What is a Solid?
What is a Sphere?
Surface Area of Prisms and Cylinders
How Do You Find the Lateral and Surface Areas of a Cylinder?
How Do You Find the Lateral and Surface Areas of a Rectangular Prism?
How Do You Find the Lateral and Surface Areas of a Triangular Prism?
How Do You Find the Surface Area of a Cylinder Using a Net?
How Do You Find the Surface Area of a Rectangular Prism Using a Net?
What is the Formula for the Surface Area of a Cylinder?
What is the Formula for the Surface Area of a Prism?
Surface Area of Pyramids and Cones
How Do You Find the Lateral and Surface Areas of a Cone if You Don't Know the Slant Height?
How Do You Find the Lateral and Surface Areas of a Cone?
How Do You Find the Lateral and Surface Areas of a Regular Pyramid?
Volume of Prisms and Cylinders
How Do You Find the Volume of a Cylinder?
How Do You Find the Volume of a Rectangular Prism?
How Do You Find the Volume of a Triangular Prism?
What is the Formula for the Volume of a Cylinder?
What is the Formula for the Volume of a Prism?
What is Volume?
Volume of Pyramids and Cones
How Do You Find the Volume of a Composite Figure?
How Do You Find the Volume of a Cone?
How Do You Find the Volume of a Rectangular Pyramid?
How Do You Find the Volume of a Triangular Pyramid?
What is the Formula for the Volume of a Cone?
What is the Formula for the Volume of a Pyramid?
Spheres
How Do You Find the Surface Area of a Sphere?
How Do You Find the Volume of a Sphere?
What is a Sphere?
What is the Formula for the Surface Area of a Sphere?
What is the Formula for the Volume of a Sphere?
Congruent and Similar Solids
What is the Relationship Between the Surface Areas of Similar Solids?
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