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 stepbystep 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. Then, complete guided practice questions 1–3 and check your answers. 
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 stepbystep 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  Then, complete this assessment and check your answers. 

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  Read this article. The table lists the common types of polygons we will encounter in geometry. 
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. Then, complete review questions 1–5 and check your answers. 
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  Then, complete this assessment and check your answers. 

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  Then, complete this assessment and check your answers. 

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  Then, complete this assessment and check your answers. 

Practice with Angles in Congruent Triangles  Complete this assessment and check your answers. 

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. Then, complete review questions 1–5 and check your answers. 
3.9: Equilateral Triangles  Equilateral Triangles  Read this article and watch the videos. Pay attention to the equilateral triangle theorem and examples 3–5. Then, complete review questions 1–4 and check your answers. 
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. Then, complete review questions 1–3 and check your answers. 
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. Then, complete review questions 1–3 and check your answers. 
4.4: Medians  Triangle Medians and Centroids  Watch this video to learn about this property of triangles. 
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  Then, complete this assessment and check your answers. 

5.1: Sum of Interior Angles of a Polygon  Quadrilaterals, Polygons, and Transformations  Read this article, which reviews types of quadrilaterals and how to calculate the sum of polygon angles. 
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. Then, complete review questions 4–15 and check your answers. 

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. 
5.6: Coordinate Geometry  Quadrilaterals  Watch these two videos on quadrilaterals and their properties. 
Practice with Quadrilaterals  Then, complete this assessment to review your knowledge of quadrilaterals and check your answers. 

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. Then, complete review questions 14–18 and check your answers. 

6.2: Similarity Postulates  Similarity Postulates  Watch this video to learn how to apply similarity postulates to triangles. 
6.3: AngleAngle Similarity and Indirect Measurement  AngleAngle 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: SideSideSide and SideAngleSide Similarity  SideSideSide Triangle Similarity  Read this article and watch the four embedded videos. Pay attention to the SideSideSide (SSS) Similarity Theorem and the examples of determining if two triangles are similar and solving for unknown values. 
SideAngleSide Triangle Similarity  Next, read this article and watch the embedded video. Pay attention to the SideAngleSide (SAS) criterion for similarity and Examples 1–3, which explain how to apply this criterion to solve for unknown values. 

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  Complete this second set of assessments and check your answers. 

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  Then, complete these practice problems and check your answers. 

7.2: 454590 Triangles  454590 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. Then, complete review questions 9–12 and check your answers. 
7.3: 306090 Right Triangles  306090 Right Triangles  Read this article and watch the videos. Pay attention to the 306090 theorem, which gives the ratio needed to solve for an unknown side of this type of triangle. Then, complete review questions 5–8 and check your answers. 
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  Then, take this assessment and check your answers. 

7.5: Trigonometric Ratios with a Calculator  Using a Calculator for Trigonometric Ratios  Read this article and watch the videos to learn how to input trigonometric functions into your calculator. 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  Then, complete this assessment and check your answers. 

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  Then, complete this assessment and check your answers. 

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. Then, complete review questions 1–10 and check your answers. 

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. Then, complete review questions 1–5 and check your answers. 
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. 
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. 
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  Read this article, which explains the circumference formula and gives examples for calculating circumference. Then, complete the practice questions and check your answers. 
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  Then, take this assessment and check your answers. 

9.11: Area of Composite Shapes  Perimeter and Area of a NonStandard 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 threedimensional solids are represented on paper and how we can map threedimensional 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. Then, complete review questions 9–12 and check your answers. 
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. Then, complete review questions 3–6 and check your answers. 
10.4: Pyramids  Pyramids  Read this article and watch the video. Note the formulas for surface area and volume of pyramids. Then, complete review questions 9–12 and check your answers. 
10.5: Cones  Cones  Read this article and watch the videos. Pay attention to the formulas for surface area and volume. Then, complete review questions 1–3 and check your answers. 
10.6: Spheres  Spheres  Read this article and watch the video. Focus on the formulas for surface area and volume. 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. 
Course Feedback Survey  Course Feedback Survey 