Topic Name Description
Course Syllabus Course Syllabus
1.1: Language and Notation The Language and Notation of Basic Geometry

Watch this video. Make sure you understand the definitions for line, line segment, ray, midpoint, collinear, and planar.

Lines, Line Segments, and Rays

This video discusses the differences between geometric objects that may appear to be similar: lines, line segments, and rays.

1.2: The Distance between Two Points The Distance between Two Points

Read this article and watch the videos. Pay attention to the sections on the ruler postulate and the segment addition postulate. These two postulates help us perform certain measurements. The videos give examples. Read the examples near the end of the page closely to see step-by-step solutions.

Then, complete review questions 1, 2, 6, 7, 9, 10, 11, 16, and 17 and check your answers.

1.3: Midpoints and Segment Bisectors Midpoints and Segment Bisectors

Read this article and watch the video to learn about these concepts. Pay close attention to the midpoint formula, since we use this formula to determine the midpoint of a segment.

1.4: Measuring Angles Angles

First, watch this video to learn the vocabulary of angles.

Measuring Angles

Once you feel comfortable with the vocabulary we use to describe angles, watch these videos to learn how to use a protractor, the tool we use to measure angles accurately. The videos also explain the units we use to define angles.

1.5: Congruent Angles and Angle Bisectors Congruent Angles and Angle Bisectors

Read this article and watch the videos. Pay attention to the section on investigation, which explains the step-by-step method for constructing an angle bisector. Carefully read the examples.

Then, complete practice questions 1, 5, 11, and 12 and check your answers.

1.6: Acute, Obtuse, and Right Angles Acute, Right, and Obtuse Angles

Watch these videos to learn about ways to classify angles based on their degree.

1.7: Complementary and Supplementary Angles Complementary and Supplementary Angles

Watch these videos. Pay close attention to the definition of complementary and supplementary used to describe sets of angles.

Practice with Complementary and Supplementary Angles

1.8: Linear Pairs Linear Pairs

Read this article and watch the videos to learn about linear pairs, adjacent angles, and angles that form a linear pair. Pay attention to the examples of how to measure angles and identify linear pairs.

Then, complete review questions 6, 7, 12, and 13 and check your answers.

1.9: Vertical Angles Vertical Angles

Watch this video to learn about vertical angles and how they relate to each other.

Equations with Vertical Angles

Then, watch this video for more advanced examples that use algebra.

Practice Solving Problems with Vertical Angles

Then, complete this assessment, which combines what you know about vertical angles with basic algebra to solve problems.

1.10: Polygon Classification Classifying Polygons

2.1: Parallel, Perpendicular, and Skew Lines Identifying Parallel and Perpendicular Lines

Watch this video to learn how to identify these types of lines.

2.2: Angles and Transversals Angles, Parallel Lines, and Transversals

Read this article and watch the video. These materials use language we will explore in later sections, but you should understand how to calculate the angle of a transversal. Pay close attention to how to calculate an unknown angle on a transversal line.

2.3: Corresponding Angles Corresponding Angles

Read this article and watch the videos. The corresponding angle postulate states that corresponding angles have approximately the same degree measurement. Watch the videos to see examples of how to calculate corresponding angles and their measurements. Carefully read examples 1–3.

Then, complete review questions 2, 3, 4, 11, 12, 13, 14, and 15 and check your answers.

2.4: Alternate Interior Angles Alternate Interior Angles

Read this article and watch the videos. Pay attention to the alternate interior angles theorem, which states that alternate interior angles are congruent. Do not focus on the proof, but pay attention to the example on measuring angles.

Then, complete review questions 1, 2, 6, 7, and 8 and check your answers.

2.5: Alternate Exterior Angles Alternate Exterior Angles

Read this article and watch the videos. Pay attention to the alternate exterior angles theorem. As in the last section, do not focus on the proofs. Rather, focus on the examples that demonstrate how to recognize alternate exterior angles, measure angles, and apply these concepts to the real world.

Then, complete review questions 1, 2, 3, 4, 13, 14, and 15 and check your answers.

2.6: Same Side Interior Angles Same Side Interior Angles

Read this article and watch the videos. Pay attention to the same side interior angle theorem. Read the examples on recognizing same side interior angles and measuring angles closely.

2.7: Distance Formula in the Coordinate Plane Using the Distance Formula

Watch this video on how to use the distance formula to find the distance between two points and a few examples of how to do it.

Practice Using the Distance Formula

After you watch the video, complete this assessment and check your answers.

3.1: Triangle Classification Triangle Classification

Read this article and watch the videos to learn how to classify triangles based on their angles and sides. Pay attention to the list of different types of triangles. It may be helpful to make a list of these different classifications of triangles and their characteristics.

3.2: Triangle Sum Theorem Using the Triangle Sum Theorem

Watch this video to see why the triangle sum theorem works.

Practice Using the Exterior Angle Theorem

3.3: Exterior Angle Theorem Using the Exterior Angle Theorem

Watch this video to see an example of how to use the exterior angle theorem.

Practice Using the Exterior Angle Theorem

3.4: Congruent Figures Congruent Figures

Read this article and watch the video. Pay attention to the steps you need to take to determine if two figures are congruent.

3.5: Congruent Triangles and SSS Congruent Triangles and the SSS Postulate

Watch this video to learn how to use the SSS postulate to determine if two triangles are congruent.

3.6: Other Triangle Congruence Postulates The SAS, ASA, and AAS Postulates

Watch this video for definitions of these postulates and examples of how to use them.

3.7: Calculating Congruent Triangles Congruent Triangles

Watch this video for examples of how to use different postulates to determine the congruence between triangles.

Practice with Congruent Triangles

Practice with Angles in Congruent Triangles

3.8: Isosceles Triangles Isosceles Triangles

Read this article and watch the videos. Pay attention to the terminology that it introduces about isosceles triangles. The base angle theorem states that the base angles of an isosceles triangle must be congruent. Do not focus on the proof. Pay attention to the examples of how to recognize congruent angles, measure vertex angles, and measure base angles.

3.9: Equilateral Triangles Equilateral Triangles

Read this article and watch the videos. Pay attention to the equilateral triangle theorem and examples 3–5.

4.1: Midsegment Theorem Midsegment Theorem

Read this article and watch the videos. Pay attention to the definitions of midsegment, the midsegment theorem, and how to calculate the length of a midsegment. Review examples 1–5 to see how to use the midsegment theorem to solve for unknown quantities in triangles.

Then, complete review questions 5, 6, 9, 10, and 16, and check your answers.

4.2: Perpendicular Bisectors Perpendicular Bisectors

Read this article and watch the videos. Pay close attention to the definition of a perpendicular bisector and the perpendicular bisector theorem, which tells us how to make a triangle out of a line segment and a perpendicular bisector. Read examples 1–5.

4.3: Angle Bisectors Angle Bisectors

Read this article and watch the videos. Pay attention to the angle bisector theorem, which states that any point on an angle bisector is equidistant to both sides of the angle. This allows us to create two identical triangles on either side of the angle bisector. Closely read examples 1–3.

4.4: Medians Triangle Medians and Centroids

Using Medians and Centroids to Solve Unknown Quantities

Watch this video to see an example of how to use medians to solve for unknown quantities in a triangle.

4.5: Altitudes Altitudes

Read this article and watch the videos. Pay attention to the figures that show how to draw altitudes for acute, right, and obtuse triangles. Carefully read examples 1–5, which describe how to draw altitudes for different types of triangles.

4.6: Triangle Inequality Theorem Triangle Inequality Theorem

Read this article and watch the videos. Focus on the examples of solving for unknown length and making conclusions about lengths of legs. Pay attention to how to determine whether a given set of lengths will form a triangle.

Practice Using the Triangle Inequality Theorem

5.1: Sum of Interior Angles of a Polygon Quadrilaterals, Polygons, and Transformations

Sum of Interior Angles of a Polygon

Now we are ready to explore the interior angles of a polygon in more detail. Watch this video for examples of how to determine the sum of the interior angles in a polygon.

5.2: Sum of Exterior Angles of a Convex Polygon Sum of Exterior Angles of a Convex Polygon

Watch this video to learn how to perform this calculation and to see examples.

Practice Adding Angles of a Polygon

Then, complete this assessment, which includes the sum of exterior angles of a polygon and the sum of interior angles of a polygon.

5.3: Parallelograms Parallelograms

Read this article and watch the videos, which review the structure and properties of parallelograms. Pay attention to the list of theorems that pertain to parallelograms. These theorems are useful when solving for unknown side lengths or angles. Closely read the sections on measuring angles and solving for unknown values. Be sure to read examples 1–3.

Then, complete review questions 1, 4, 5, 16, 17, 18, and 19 and check your answers.

Classifying Parallelograms

We can classify different types of parallelograms based on their properties. Read this article and watch the video. Pay attention to the definitions for rectangle, rhombus, and square.

5.4: Trapezoids Trapezoids

Read this article and watch the video. Pay attention to the special form of the midsegment theorem as it applies to trapezoids. Closely read examples 1–5.

Then, complete review questions 2, 3, and 8 and check your answers.

5.5: Kites Kites
Read this article and watch the two embedded videos which describe the properties of kites and shows various examples. Pay attention to the examples on measuring angles, using the Pythagorean theorem, and finding the missing angle. Closely read examples 1–3.

After you have reviewed the material, complete review questions 1, 2, 7, and 8 and check your answers.

Watch these two videos on quadrilaterals and their properties.

6.1: Similar Polygons Similar Triangles

First, watch this video, which describes the meaning of similarity and applies its definition to triangles, the simplest polygon.

Similar Polygons and Scale Factors

Next, read this article and watch the videos, which also define similarity for polygons. The first video offers an example of using similarity to solve for unknown values in a polygon. Closely read example 1.

6.2: Similarity Postulates Similarity Postulates

Watch this video to learn how to apply similarity postulates to triangles.

6.3: Angle-Angle Similarity and Indirect Measurement Angle-Angle Similarity Postulate

Read this article and watch the videos, which define AA similarity. Examples 1–5 show how to apply the AA similarity postulate to solve for unknowns in a triangle.

Then, complete review questions 6, 7, 8 and 10 and check your answers.

6.4: Side-Side-Side and Side-Angle-Side Similarity Side-Side-Side Triangle Similarity

Read this article and watch the four embedded videos. Pay attention to the Side-Side-Side (SSS) Similarity Theorem and the examples of determining if two triangles are similar and solving for unknown values.

After you have reviewed the material, complete review questions 11–16 and check your answers.

Side-Angle-Side Triangle Similarity

Next, read this article and watch the embedded video. Pay attention to the Side-Angle-Side (SAS) criterion for similarity and Examples 1–3, which explain how to apply this criterion to solve for unknown values.

After you have reviewed the material, complete review questions 5–10 and check your answers.

6.5: Triangle Proportionality, Parallel Lines and Transversals Solving Similar Triangles

Watch this video to see examples of problems where the similarity criteria are used to determine side lengths and angles of triangles.

Practice Solving Similar Triangles Part I

After you have watched the video, complete these assessments to test what you have learned and check your answers.

Practice Solving Similar Triangles Part II

7.1: The Pythagorean Theorem The Pythagorean Theorem

Watch this introductory video.

Using the Pythagorean Theorem

Watch this video on how to use the Pythagorean theorem to solve for the length of an unknown side of a triangle.

Practice Using the Pythagorean Theorem

7.2: 45-45-90 Triangles 45-45-90 Right Triangles

Read this article and watch the videos to learn about the special properties of isosceles triangles. Pay attention to the examples of finding the length of missing side and solving for unknowns. The article also shows how we can divide squares into two isosceles triangles and then use our knowledge of these triangles to solve for an unknown.

7.3: 30-60-90 Right Triangles 30-60-90 Right Triangles

Read this article and watch the videos. Pay attention to the 30-60-90 theorem, which gives the ratio needed to solve for an unknown side of this type of triangle.

7.4: Sine, Cosine, and Tangent Trigonometry

Read this page and watch the video. This gives a good overview of the three main trigonometric functions: sine, cosine, and tangent. It may be helpful to write the definitions down for yourself to keep track of them.

Practice Trigonometric Ratios in Right Triangles

7.5: Trigonometric Ratios with a Calculator Using a Calculator for Trigonometric Ratios

Then, complete review questions 1–3 and check your work to make sure you are able to use your calculator correctly.

8.1: Language and Notation of a Circle Circle Language and Notation

Watch this video to become familiar with the terms we will use in this unit.

8.2: Tangent Lines Tangent Lines

Read this article and watch the videos to learn about the tangent line theorem, which defines tangent lines, and the two tangents theorem, which we use to solve for unknown lengths of line segments. Read examples 1–5 closely to see how to draw tangent lines and how we can use tangent lines to solve for unknown quantities.

Then, complete review questions 1, 2, 4, and 5 and check your answers.

8.3: Arcs of Circles Arcs

Watch these videos, which introduce the idea of arcs in circles and give examples of how to determine the angle of a given arc.

Practice Measuring Arcs

8.4: Inscribed Angles Value of Inscribed Angles and Polygons

Read this brief article, which gives an overview of what inscribed angles are and how to identify them. Watch the video to see how to use your knowledge of triangles to determine the value of inscribed angles.

Practice Inscribed Angles and Polygons

8.5: Angles of Chords, Secants, and Tangents Chords in Circles

Read this article and watch the video. Pay attention to the examples of how to determine the lengths of chords and their angles. It may help to write down the four chord theorems to help you keep track of them as you work through the problems.

Angles of Chords, Secants, and Tangents

Once you feel comfortable with the definition of chords and their theorems, read this article which details several ways we can calculate the angles formed by chords. Since this page has so much information, read slowly and take time to work through each example. It may be helpful to write down the many theorems to make sure you understand them.

9.1: Perimeter and Area Basics Perimeter and Area Basics

Watch this video to learn how mathematicians talk about these concepts.

9.2: Area of Triangles Area and Perimeter of a Triangle

Read this article and watch the videos. Pay attention to the formula for the area of a triangle, including the special case of right triangles. Note that we use the Pythagorean theorem to calculate the perimeter of a triangle.

9.3: Area and Perimeter of Rectangles and Squares Area and Perimeter of a Rectangle

Read this article and watch the three embedded videos, which discuss the formulas we use to calculate the area and perimeter of rectangles and squares.

After you have reviewed the material, complete review questions 1–6 and check your answers.

9.4: Area of a Parallelogram Area of a Parallelogram

Read this article and watch the videos. Pay attention to how to "rearrange" a parallelogram into rectangles before calculating its area.

Then, complete review questions 1, 2, 6, 7, 13, and 14 and check your answers.

9.5: Area and Perimeter of Trapezoids Area and Perimeter of Trapezoids

Read this article and watch the two embedded videos, which highlight the formulas we use to calculate the area and perimeter of a trapezoid.

After you have reviewed the material, complete review questions 1–5 and check your answers.

9.6: Area and Perimeter of Rhombuses and Kites Area and Perimeter of Rhombuses and Kites

Read this article and watch the video which highlight the formulas we use to calculate the area and perimeter of rhombuses and kites.

Then, complete review questions 2, 3, 4, 12, 13, 14, and 15 and check your answers.

9.7: Area and Perimeter of Similar Polygons Area and Perimeter of Similar Polygons

Read this article and watch the video. These highlight the formulas we use to calculate the area and perimeter of similar polygons. Perimeters and areas of similar polygons are proportional.

9.8: Circumference Circumference Review

9.9: Arc Length Arc Length

Read this article and watch the videos. Note the arc length formula. Pay attention to the examples on measuring arc length, finding the radius, and measuring the central angle.

Then, complete review questions 1, 5, and 8 and check your answers.

9.10: Area of a Circle Area of a Circle

Watch this video, which introduces the formula for the area of a circle and an example of using this formula.

Practice Calculating the Area of a Circle

9.11: Area of Composite Shapes Perimeter and Area of a Non-Standard Polygon

Watch this video to see how we can use what we learned about standard polygons to develop methods for determining the area and perimeter of a composite shape.

10.1: Polyhedrons Polyhedrons

Read this article and watch the video which define different common types of polyhedrons. These also cover Euler's theorem, which defines the number of faces and vertices in a given polyhedron.

Representing Solids

Read this article, which explains how three-dimensional solids are represented on paper and how we can map three-dimensional solids to two dimensions.

10.2: Prisms Prisms

Read this article and watch the videos. Focus on the definitions for surface area and volume in the text. Carefully read the examples of finding surface area and volume.

10.3 Cylinders Cylinders

Read this article and watch the videos. Make note of the formulas for the surface area of a right cylinder and the volume of a cylinder.

10.4: Pyramids Pyramids

Read this article and watch the video. Note the formulas for surface area and volume of pyramids.

10.5: Cones Cones

Read this article and watch the videos. Pay attention to the formulas for surface area and volume.

10.6: Spheres Spheres

Then, complete review questions 4, 5, 10, 12, and 13 and check your answers.

10.7: Composite Solids Composite Solids

Read this article and watch the video. Focus on the examples of how we can break composite solids down into standard shapes.

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