Illustrative Math Alignment: Grade 7 Unit 7
Angles, Triangles, and Prisms
Lesson 1: Relationships of Angles
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 7 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 7TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
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Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 8 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 8TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
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Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 9 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 9TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 1 | Solving Equations with Angle Measures 2--Example 1TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 10 | Solving Equations with Angle Measures 2--Example 10TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 2 | Solving Equations with Angle Measures 2--Example 2TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 3 | Solving Equations with Angle Measures 2--Example 3TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 4 | Solving Equations with Angle Measures 2--Example 4TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 5 | Solving Equations with Angle Measures 2--Example 5TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 6 | Solving Equations with Angle Measures 2--Example 6TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 7 | Solving Equations with Angle Measures 2--Example 7TopicEquations DescriptionThis example demonstrates solving equations involving angle measures in a kite. A kite has two pairs of adjacent congruent angles. In this case, we have angles represented as (x+50)°, (x+50)°, (y+20)°, and y°. To solve this problem, we apply two key principles: the sum of angles in a quadrilateral is 360°, and the sum of the angles of a triangle is 180°. You can use the triangle equation to solve for y. Once you determine the value for y, you can use that to find x using either the triangle or the quadrilateral equation. In the solution shown, the triangle equation is used. |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 8 | Solving Equations with Angle Measures 2--Example 8TopicEquations DescriptionThis example illustrates solving equations involving angle measures in a kite. The kite has two known angles of 70° and 40°, and two unknown angles represented as (x+y)°. To solve this problem, we look at the triangles formed by one of the diagonals of the kite and use the triangle equation. First solve for x with the top triangle. Once you find x, use that value to solve for y in the bottom triangle. You could also use the quadrilateral equation to solve for y. |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 9 | Solving Equations with Angle Measures 2--Example 9TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 1 | Solving Equations with Angle Measures--Example 1TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 10 | Solving Equations with Angle Measures--Example 10TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 11 | Solving Equations with Angle Measures--Example 11TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 12 | Solving Equations with Angle Measures--Example 12TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 13 | Solving Equations with Angle Measures--Example 13TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 14 | Solving Equations with Angle Measures--Example 14TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 15 | Solving Equations with Angle Measures--Example 15TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 2 | Solving Equations with Angle Measures--Example 2TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 3 | Solving Equations with Angle Measures--Example 3TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 4 | Solving Equations with Angle Measures--Example 4TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 5 | Solving Equations with Angle Measures--Example 5TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 6 | Solving Equations with Angle Measures--Example 6TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 7 | Solving Equations with Angle Measures--Example 7TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 8 | Solving Equations with Angle Measures--Example 8TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 9 | Solving Equations with Angle Measures--Example 9TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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MATH EXAMPLES--Teacher's Guide: Quadrilateral Classification | MATH EXAMPLES--Teacher's Guide: Quadrilateral Classification
This set of tutorials provides 34 examples of the types of quadrilaterals and how to classify quadrilaterals based on the sides and angles. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Definition of a Quadrilateral |
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MATH EXAMPLES--Teacher's Guide: Right Triangles | MATH EXAMPLES--Teacher's Guide: Right Triangles
This set of tutorials provides 26 examples of how to find the length of a side of a triangle using given angle or side measurements. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Right Triangles |
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Promethean Flipchart: Geometry Applications: Angles | Himeji castle in Japan is a marvel of architecture and a startling example of geometry and military science. The castle was used to protect samurai armies from invading forces, and the use of acute, obtuse, and right angles as part of the defense structure provide many opportunities for exploring the nature of geometric angles. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Angles and Planes, Segment 2: Angles]: https://www.media4math.com/library/geometry-applications-angles-and-planes-segment-2-angles |
Applications of Angles and Planes |
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Promethean Flipchart: Geometry Applications: Right Triangles | The ancient port city of Corinth in Greece allows us to explore the evolution of sailing. The shapes of sails went from rectangular to triangular. The use of right-triangle-shaped sails changed the nature of sailing. Becoming less reliant on oarsmen and being able to sail under nearly any wind conditions, the sailboat made the conquest of the seas possible. We explore the properties of right triangles that make such sails ideal. Note: The download for this resources is the Promethean Flipchart. A full video is available here [Geometry Applications: Triangles, Segment 3: Right Triangles]: https://media4math.com/library/geometry-applications-triangles-segment-3-right-triangles |
Applications of Triangles |
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Promethean Flipchart: Geometry Applications: Triangles | The Eiffel Tower includes quite a number of exposed triangular trusses. The properties of triangles are used to explore and explain the frequent use of triangular trusses in many building. In particular, isosceles and equilateral triangular trusses are explored. In addition triangle postulates and similarity are explored and analyzed. Note: The download for this resources is the Promethean Flipchart. This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-triangles To view the video Geometry Applications: Triangles: https://www.media4math.com/library/geometry-applications-triangles |
Applications of Triangles |
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Test Prep Interactive Quiz--Classifying Angles | Test Prep Interactive Quiz--Classifying Angles
This is part of a collection of self-scoring interactive math quizzes on a variety of topics. To see the complete of these quizzes, click on this link. Note: The download is the teacher's guide.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Definition of an Angle |
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Video Transcript: Desmos Geometry Exploration: Angles | Video Transcript: Desmos Geometry Exploration: Angles
This is the transcript for the video entitled, Desmos Geometry Exploration: Angles. In this video tutorial angles are defined. Students are shown how to construct and measure using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry. This is part of a collection of video transcript for the video tutorial series on using the Desmos Geometry Tools. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Definition of an Angle |
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Video Transcript: Desmos Geometry Exploration: Classifying Triangles by Angle | This is the transcript for the video entitled, Desmos Geometry Exploration: Classifying Triangle by Angle. In this video tutorial triangles are classified by the types of angles that make up the triangle. Students are then shown how to construct such triangles using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry. The video is available for this tutorial at this link: https://www.media4math.com/library/video-tutorial-desmos-geometry-exploration-classifying-triangles-angle. Note: The download is a PDF file. Related ResourcesTo see additional resources on this topic click on the Related Resources tab above. Desmos CollectionTo see the complete collection of Desmos Resources go to this link: https://www.media4math.com/desmos-resources. Note: The download is a PDF file. |
Geometric Constructions with Triangles and Definition of a Triangle |
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Video Transcript: Desmos Geometry Exploration: Classifying Triangles by Side Length | Video Transcript: Desmos Geometry Exploration: Classifying Triangles by Side Length
This is the transcript for the video entitled, Desmos Geometry Exploration: Classifying Triangle by Side. In this video tutorial triangles are classified by the side lengths that make up the triangle. Students are then shown how to construct such triangles using the Desmos geometry tools. |
Geometric Constructions with Triangles and Definition of a Triangle |
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Video Transcript: Desmos Geometry Exploration: Types of Angles I | Video Transcript: Desmos Geometry Exploration: Types of Angles I
This is the transcript for the video entitled, Desmos Geometry Exploration: Types of Angles I. In this video tutorial different types of angles are defined, including acute, right, supplementary, and straight angles. Students are shown how to construct these types of angles using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry. |
Definition of an Angle |
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Video Transcript: Desmos Geometry Exploration: Types of Angles II | Video Transcript: Desmos Geometry Exploration: Types of Angles II
This is the transcript for the video entitled, Desmos Geometry Exploration: Types of Angles II. In this video tutorial different types of angles are defined, including adjacent angles, complementary angles, supplementary angles, and vertical angles. Students are shown how to construct these types of angles using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry. |
Definition of an Angle |
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Video Transcript: Geometry Applications: Angles and Planes | Video Transcript: Geometry Applications: Angles and Planes
This is the transcript for the video of same title. Video contents: In this program we explore the properties of angles and planes. We do this in the context of two real-world applications. In the first, we explore Japan's Himeji Castle and in the process learn about different types of angles and how they're used in a defensive fortification. In the second applicaiton we explore sedimentary rock layers as examples of parallel planes. We explore the Burgess Shale fossils. |
Definition of an Angle and Applications of Angles and Planes |
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Video Transcript: Geometry Applications: Angles and Planes, Segment 1: Introduction | Video Transcript: Geometry Applications: Angles and Planes, Segment 1: Introduction
This is the transcript for the video of same title. Video contents: The observatory in Arecibo, Puerto Rico provides astronomers insights into the structure of our solar system. Geometrically, the solar system relies on the plane known as the ecliptic. In studying the Earth's orbit it is important to know that the Earth's axis of rotation is at an angle relative to the ecliptic. This segment introduces the key themes of the program. |
Applications of Points and Lines |
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Video Transcript: Geometry Applications: Angles and Planes, Segment 2: Angles | Video Transcript: Geometry Applications: Angles and Planes, Segment 2: Angles
This is the transcript for the video of same title. Video contents: Himeji castle in Japan is a marvel of architecture and a startling example of geometry and military science. The castle was used to protect samurai armies from invading forces, and the use of acute, obtuse, and right angles as part of the defense structure provide many opportunities for exploring the nature of geometric angles. |
Applications of Points and Lines |
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Video Transcript: Geometry Applications: Angles and Planes, Segment 3: Planes | Video Transcript: Geometry Applications: Angles and Planes, Segment 3: Planes
This is the transcript for the video of same title. Video contents: In the Canadian Rockies, the Burgess Shale fossils provide a window to prehistoric Earth. Fossil layers are folded into sedimentary rocks. And sedimentary rocks are examples of parallel planes. This segment uses the properties of planes to analyze fossils. |
Applications of Points and Lines |
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Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles | Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles
This is the transcript for the video of same title. Video contents: The Roman Pantheon is a domed structure that shows a keen awareness of the position of the sun throughout the year. The source of light from the top of the dome allows for the exploration of chords, inscribed angles, central angles, and intercepted arcs. |
Applications of Circles |
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Video Transcript: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles | Video Transcript: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles
This is the transcript for the video of same title. Video contents: Frank Lloyd Wright's architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure. |
Applications of Quadrilaterals |
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Video Transcript: Geometry Applications: Triangles | Video Transcript: Geometry Applications: Triangles
This is the transcript for the video of same title. Video contents: In this program we explore the properties of triangle. We do this in the context of two real-world applications. In the first, we explore the triangular trusses in the Eiffel Tower and in the process learn about key properties of triangles. In the second application, we look at right-triangle-shaped sails on sail boat and why these are the ideal shape for efficient sailing. |
Applications of Triangles |
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Video Transcript: Geometry Applications: Triangles, Segment 1: Introduction | Video Transcript: Geometry Applications: Triangles, Segment 1: Introduction
This is the transcript for the video of same title. Video contents: The Bank of China building in Hong Kong is a dramatic example of triangular support. The notion of triangular trusses is introduced, along with the key concepts developed in the rest of the program. This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Applications of Triangles |
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Video Transcript: Geometry Applications: Triangles, Segment 2: Triangles | Video Transcript: Geometry Applications: Triangles, Segment 2: Triangles
This is the transcript for the video of same title. Video contents: The Eiffel Tower includes quite a number of exposed triangular trusses. The properties of triangles are used to explore and explain the frequent use of triangular trusses in many building. In particular, isosceles and equilateral triangular trusses are explored. In addition triangle postulates and similarity are explored and analyzed. |
Applications of Triangles |
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Video Transcript: Geometry Applications: Triangles, Segment 3: Right Triangles | Video Transcript: Geometry Applications: Triangles, Segment 3: Right Triangles
This is the transcript for the video of same title. Video contents: The ancient port city of Corinth in Greece allows us to explore the evolution of sailing. The shapes of sails went from rectangular to triangular. The use of right-triangle-shaped sails changed the nature of sailing. Becoming less reliant on oarsmen and being able to sail under nearly any wind conditions, the sailboat made the conquest of the seas possible. We explore the properties of right triangles that make such sails ideal. |
Applications of Triangles |
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Video Transcript: Ratios and Proportions: Scale Drawings | Video Transcript: Ratios and Proportions: Scale Drawings
This is the transcript that goes with the video segment entitled Video Tutorial: Ratios and Proportions: Scale Drawings. This is part of a collection of video transcripts for the video tutorial series on Ratios. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Ratios and Rates |
