Illustrative Math Alignment: Grade 7 Unit 7
Angles, Triangles, and Prisms
Lesson 9: Drawing Triangles (Part 1)
Use the following Media4Math resources with this Illustrative Math lesson.
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Definition--Triangle Concepts--Pythagorean Triples | Pythagorean TriplesTopicTriangles DefinitionPythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem: a2 + b2 = c2 DescriptionPythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Common examples include (3, 4, 5) and (5, 12, 13). |
Definition of a Triangle |
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Definition--Triangle Concepts--Right Triangle | Right TriangleTopicTriangles DefinitionA right triangle is a triangle with one 90-degree angle. DescriptionA right triangle is a type of triangle that has one angle measuring 90 degrees. This type of triangle is fundamental in geometry and trigonometry, as it forms the basis for the Pythagorean theorem: a2 + b2 = c2 This concept is essential in various real-world applications, such as in construction and navigation. For example, right triangles are used to create right angles and ensure accuracy in building projects. They also play a crucial role in various mathematical problems and proofs. |
Definition of a Triangle |
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Definition--Triangle Concepts--Scalene Triangle | Scalene TriangleTopicTriangles DefinitionA scalene triangle is a triangle with all three sides of different lengths and all three angles of different measures. DescriptionA scalene triangle is characterized by having all three sides of different lengths and all three angles of different measures. This type of triangle is significant in geometry as it represents a unique class of triangles with specific properties. |
Definition of a Triangle |
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Definition--Triangle Concepts--Similar Triangles | Similar TrianglesTopicTriangles DefinitionSimilar triangles are triangles that have the same shape but not necessarily the same size, with corresponding angles equal and corresponding sides proportional. DescriptionSimilar triangles are fundamental in geometry, representing triangles that have the same shape but not necessarily the same size. This means that all corresponding angles are equal, and all corresponding sides are proportional. |
Definition of a Triangle |
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Definition--Triangle Concepts--Triangle Altitude | Triangle AltitudeTopicTriangles DefinitionThe altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side. DescriptionThe altitude of a triangle is a significant concept in geometry, representing the perpendicular distance from a vertex to the line containing the opposite side. This measurement is crucial in various geometric calculations, such as finding the area of a triangle. |
Definition of a Triangle |
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Definition--Triangle Concepts--Triangle Height | Triangle HeightTopicTriangles DefinitionThe height of a triangle is the perpendicular distance from a vertex to the line containing the opposite side, often used interchangeably with altitude. DescriptionThe height of a triangle, often used interchangeably with altitude, is a crucial concept in geometry. It represents the perpendicular distance from a vertex to the line containing the opposite side. This measurement is essential for calculating the area of a triangle, using the formula: Area= 1/2 × base × height |
Definition of a Triangle |
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Definition--Triangle Concepts--Triangle Inscribed in a Circle | Triangle Inscribed in a CircleTopicTriangles DefinitionA triangle inscribed in a circle is a triangle whose vertices all lie on the circumference of the circle. DescriptionA triangle inscribed in a circle, also known as a circumtriangle, is a triangle whose vertices all lie on the circumference of the circle. The circle is called the circumcircle, and its center is the circumcenter of the triangle. |
Definition of a Triangle |
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Definition--Triangle Concepts--Triangle, Definition 1 | Triangle, Definition 1TopicTriangles DefinitionA triangle is a polygon with three edges and three vertices. DescriptionA triangle is one of the simplest and most fundamental shapes in geometry, characterized by having three sides and three vertices. The sum of the interior angles of a triangle is always 180 degrees, which is a key property used in various geometric proofs and constructions. In real-world applications, triangles are used extensively in engineering, architecture, and design due to their inherent stability and strength. For example, triangular structures are often used in bridges and roof trusses to distribute weight evenly and provide support. |
Definition of a Triangle |
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Definition--Triangle Concepts--Triangle, Definition 2 | Triangle, Definition 2TopicTriangles DefinitionA triangle is a three-sided polygon with three vertices and three angles. DescriptionA triangle is a three-sided polygon that is fundamental in the study of geometry. Each triangle has three vertices and three angles, and the sum of its interior angles is always 180 degrees. This property is crucial for understanding various geometric principles and solving related problems. |
Definition of a Triangle |
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Definition--Triangle Concepts--Vertex of a Triangle | Vertex of a TriangleTopicTriangles DefinitionA vertex of a triangle is a point where two sides of the triangle meet. DescriptionA vertex of a triangle is one of the three points where the sides of the triangle intersect. Each triangle has three vertices, and these points are crucial for defining the shape and properties of the triangle. |
Definition of a Triangle |
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INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Constructing an Isosceles Triangle | In this Slide Show, we show how to construct an isosceles triangle. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT. |
Definition of a Triangle and Geometric Constructions with Triangles |
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INSTRUCTIONAL RESOURCE: Nspire App Tutorial: The Perpendicular Bisectors of a Triangle | In this Slide Show, we show how to construct the perpendicular bisectors of the three sides of a triangle to show they intersect at a single point. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT. |
Definition of a Triangle and Geometric Constructions with Triangles |
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INSTRUCTIONAL RESOURCE: TI-Nspire App Activity: Constructing an Isosceles Triangle | In this Slide Show, learn how to use the TI-Nspire App to construct an isosceles triangle. Note: The download is a PPT file. |
Definition of a Triangle and Geometric Constructions with Triangles |
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Interactive Crossword Puzzle--Triangles | Interactive Crossword Puzzle--Triangles
This interactive crossword puzzle tests knowledge of key terms on the topic of triangles. This is part of a collection of math games and interactives. To see the complete collection of the games, 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. |
Definition of a Triangle |
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Interactive Math Game: Math Riddles--Triangles | Interactive Math Game: Math Riddles--Triangles
In this Math Riddles Game, have your students review vocabulary around the topic of triangles. The Math Riddles games are useful for practicing: Math Vocabulary, Key Concepts, Critical Thinking. This is part of a collection of math games and interactives. To see the complete collection of the games, 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. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 1 | Math Example--Polygons--Triangle Classification: Example 1
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 10 | Math Example--Polygons--Triangle Classification: Example 10
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 11 | Math Example--Polygons--Triangle Classification: Example 11
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 12 | Math Example--Polygons--Triangle Classification: Example 12
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 13 | Math Example--Polygons--Triangle Classification: Example 13
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 14 | Math Example--Polygons--Triangle Classification: Example 14
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 15 | Math Example--Polygons--Triangle Classification: Example 15
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 16 | Math Example--Polygons--Triangle Classification: Example 16
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 17 | Math Example--Polygons--Triangle Classification: Example 17
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 18 | Math Example--Polygons--Triangle Classification: Example 18
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 19 | Math Example--Polygons--Triangle Classification: Example 19
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 2 | Math Example--Polygons--Triangle Classification: Example 2
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 20 | Math Example--Polygons--Triangle Classification: Example 20
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 21 | Math Example--Polygons--Triangle Classification: Example 21
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 22 | Math Example--Polygons--Triangle Classification: Example 22
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 23 | Math Example--Polygons--Triangle Classification: Example 23
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 24 | Math Example--Polygons--Triangle Classification: Example 24
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 3 | Math Example--Polygons--Triangle Classification: Example 3
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 4 | Math Example--Polygons--Triangle Classification: Example 4
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 5 | Math Example--Polygons--Triangle Classification: Example 5
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 6 | Math Example--Polygons--Triangle Classification: Example 6
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 7 | Math Example--Polygons--Triangle Classification: Example 7
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 8 | Math Example--Polygons--Triangle Classification: Example 8
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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Math Example--Polygons--Triangle Classification: Example 9 | Math Example--Polygons--Triangle Classification: Example 9
This is part of a collection of math examples that focus on geometric shapes. |
Definition of a Triangle |
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MATH EXAMPLES--Teacher's Guide: Triangle Classification | MATH EXAMPLES--Teacher's Guide: Triangle Classification
This set of tutorials provides 24 examples that show how to identify different types of triangles and how to solve for x using the properties of triangles. 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 Triangle |
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MATH EXAMPLES--Triangle Classification | MATH EXAMPLES--Triangle Classification
This set of tutorials provides 24 examples that show how to identify different types of triangles and how to solve for x using the properties of triangles. NOTE: The download is a PPT file. |
Definition of a Triangle |
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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: Triangle Basics | Video Transcript: Desmos Geometry Exploration: Triangle Basics
This is the transcript for the video entitled, Desmos Geometry Exploration: Triangle Basics. In this video tutorial the basics of triangles are explored. Students are then shown how to construct triangles using the Desmos geometry tools. 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 a Triangle and Geometric Constructions with Triangles |
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Video Transcript: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle | Video Transcript: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle
This is the transcript for the TI-Nspire Mini-Tutorial entitled, Circumscribing a Circle about a Triangle. This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. 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. |
Geometric Constructions with Triangles |
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Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Circumcenter of a Triangle | Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Circumcenter of a Triangle
This is the transcript for the TI-Nspire Mini-Tutorial entitled, Constructing the Circumcenter of a Triangle. This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. 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. |
Geometric Constructions with Triangles |
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Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Orthocenter of a Triangle | Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Orthocenter of a Triangle
This is the transcript for the TI-Nspire Mini-Tutorial entitled, Constructing the Orthocenter of a Triangle. This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. 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. |
Geometric Constructions with Triangles |
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Video Tutorial: Desmos Geometry Exploration: Classifying Triangles by Angle | Video Tutorial: Desmos Geometry Exploration: Classifying Triangles by Angle
This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts. |
Definition of a Triangle and Geometric Constructions with Triangles |
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Video Tutorial: Desmos Geometry Exploration: Classifying Triangles by Side Length | Video Tutorial: Desmos Geometry Exploration: Classifying Triangles by Side Length
This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts. |
Geometric Constructions with Triangles |
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Video Tutorial: Desmos Geometry Exploration: Triangle Basics | Video Tutorial: Desmos Geometry Exploration: Triangle Basics
This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts. |
Definition of a Triangle and Geometric Constructions with Triangles |
