Illustrative Math Alignment: Grade 7 Unit 7

Angles, Triangles, and Prisms

Lesson 8: Triangles with 3 Common Measures

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Animated Math Clip Art--3D Geometry--Rotating a Triangle to Form a Cone	Rotating a Triangle to Form a Cone Topic 3D Geometry Description This animation shows how rotating a triangle around one of its sides creates a cone. It's a powerful visualization of how 2D shapes can generate 3D objects through rotation. Animated math clip art like this is crucial for teaching as it helps students visualize the formation of cones. Teachers can use this to introduce concepts of volume and surface area of cones, as well as topics in calculus related to solids of revolution.	Cones
Animated Math Clip Art--Triangles--Acute Triangles 1	Animated Math Clip Art--Triangles--Acute Triangles 1 Topic Triangles Description This animated clip art illustrates an acute triangle, where all angles are less than 90 degrees. Such visual aids are crucial for understanding the properties of triangles, particularly in identifying different types of triangles based on angles. By incorporating this image into lessons, students can visually distinguish acute triangles from other types, enhancing their comprehension through dynamic representation.	Definition of a Triangle
Animated Math Clip Art--Triangles--Acute Triangles 2	Animated Math Clip Art--Triangles--Acute Triangles 2 Topic Triangles Description This animated clip art features another example of an acute triangle, reinforcing the concept that all angles are less than 90 degrees. Visualizing different acute triangles helps students grasp the range of shapes these triangles can take, promoting a better understanding of geometric diversity. Using animated math clip art in teaching not only clarifies concepts but also stimulates student interest. The animation provides a dynamic learning experience, making it easier for students to remember and apply their knowledge of triangles. Teachers can leverage this tool to create interactive lessons that encourage active participation.	Definition of a Triangle
Animated Math Clip Art--Triangles--Equilateral Triangles 1	Animated Math Clip Art--Triangles--Equilateral Triangles 1 Topic Triangles Description This animation showcases an equilateral triangle, where all sides and angles are equal. This clip art is helpful in teaching the unique properties of equilateral triangles, helping students understand symmetry and equality in geometry. Animated math clip art is a powerful educational tool, particularly for visual learners. It brings static concepts to life, making them more accessible and memorable. Teachers can use this animation to explain symmetry and congruence, fostering a deeper appreciation for geometric principles.	Definition of a Triangle
Animated Math Clip Art--Triangles--Equilateral Triangles 2	Animated Math Clip Art--Triangles--Equilateral Triangles 2 Topic Triangles Description This animated image depicts another equilateral triangle, reinforcing the concept of equal sides and angles. Such animations help students visualize and understand the concept of congruence and symmetry in equilateral triangles. Incorporating animated math clip art into lessons enhances student engagement and understanding. The animation provides a clear and captivating representation of geometric concepts, making it easier for students to grasp and retain information. Teachers can use this clip art to facilitate discussions about the properties of equilateral triangles.	Definition of a Triangle
Animated Math Clip Art--Triangles--Exterior Angle Theorem 1	Animated Math Clip Art--Triangles--Exterior Angle Theorem 1 Topic Triangles Description This animation illustrates the Exterior Angle Theorem, which states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. The animation dynamically shows the exterior angle being formed and highlights the relationship between the angles, making it easier for students to grasp this fundamental geometric theorem.	Definition of a Triangle
Animated Math Clip Art--Triangles--Exterior Angle Theorem 2	Animated Math Clip Art--Triangles--Exterior Angle Theorem 2 Topic Triangles Description This animation further explores the Exterior Angle Theorem, reinforcing the concept that the exterior angle is the sum of the two non-adjacent interior angles. The animation provides a clear visual representation, helping students to see the theorem in action and understand its application in solving geometric problems. The color-coded angles are measured on a protractor. Using animated math clip art enhances student engagement and understanding by providing a dynamic and interactive way to learn. Teachers can use this animation to encourage students to explore and apply the theorem in various contexts.	Definition of a Triangle
Animated Math Clip Art--Triangles--Isosceles Triangles 1	Animated Math Clip Art--Triangles--Isosceles Triangles 1 Topic Triangles Description This animation shows an isosceles triangle, characterized by two equal sides and two equal angles. The animation highlights these equal elements, helping students to identify and understand the properties of isosceles triangles. This visual aid is crucial for recognizing symmetry and congruence in geometry. Animated math clip art provides a captivating way to teach geometric concepts, making them more memorable and understandable for students. Teachers can use this animation to discuss the properties of isosceles triangles and their applications.	Definition of a Triangle
Animated Math Clip Art--Triangles--Isosceles Triangles 2	Animated Math Clip Art--Triangles--Isosceles Triangles 2 Topic Triangles Description This animation provides another example of an isosceles triangle, emphasizing the equal sides and angles. The animation helps students to visualize and understand the characteristics of isosceles triangles, reinforcing their ability to identify these triangles in various contexts. The color-coded angles and sides are measured. Incorporating animated math clip art into lessons engages students and enhances their understanding of geometric concepts. Teachers can use this animation to encourage students to explore the properties and applications of isosceles triangles.	Definition of a Triangle
Animated Math Clip Art--Triangles--Obtuse Triangles 1	Animated Math Clip Art--Triangles--Obtuse Triangles 1 Topic Triangles Description This animation depicts an obtuse triangle, where one angle is greater than 90 degrees. The animation highlights the obtuse angle, helping students to identify and understand the properties of obtuse triangles. This visual representation is essential for distinguishing obtuse triangles from other types. Animated math clip art is an effective tool for teaching geometric concepts, making them more engaging and comprehensible for students. Teachers can use this animation to discuss the properties and applications of obtuse triangles.	Definition of a Triangle
Animated Math Clip Art--Triangles--Obtuse Triangles 2	Animated Math Clip Art--Triangles--Obtuse Triangles 2 Topic Triangles Description This animation illustrates another obtuse triangle, focusing on the angle greater than 90 degrees. The animation helps students to visualize and understand the characteristics of obtuse triangles, reinforcing their ability to identify these triangles in different scenarios. Using animated math clip art in teaching enhances student engagement and understanding by providing a dynamic and interactive learning experience. Teachers can use this animation to facilitate discussions about the properties of obtuse triangles.	Definition of a Triangle
Animated Math Clip Art--Triangles--Pythagorean Theorem 1	Animated Math Clip Art--Triangles--Pythagorean Theorem 1 Topic Triangles Description This animation demonstrates the Pythagorean Theorem, showing the relationship between the sides of a right triangle. The animation visually represents the theorem, illustrating how the square of the hypotenuse equals the sum of the squares of the other two sides. This helps students to understand and apply the theorem in solving problems. Animated math clip art is a powerful educational tool, providing a clear and engaging way to learn complex concepts. Teachers can use this animation to explain the Pythagorean Theorem and its applications in geometry.	Definition of a Triangle
Animated Math Clip Art--Triangles--Pythagorean Theorem 2	Animated Math Clip Art--Triangles--Pythagorean Theorem 2 Topic Triangles Description This animation further explores the Pythagorean Theorem, reinforcing the concept with another example. The animation helps students to visualize the theorem in action, making it easier to understand and apply in various contexts. Incorporating animated math clip art into lessons engages students and enhances their understanding of mathematical concepts. Teachers can use this animation to encourage students to explore and apply the Pythagorean Theorem in different scenarios. Teacher’s Script: "Observe how the Pythagorean Theorem is applied in this triangle. How might this help us in real-world situations?"	Definition of a Triangle
Animated Math Clip Art--Triangles--Right Triangle Area 1	Animated Math Clip Art--Triangles--Right Triangle Area 1 Topic Triangles Description This animation shows how to calculate the area of a right triangle. The animation demonstrates the formula for area, emphasizing the base and height, and how they are used to find the area. This visual aid helps students understand the concept of area and its calculation in right triangles. Animated math clip art provides a dynamic way to teach mathematical concepts, making them more engaging and understandable for students. Teachers can use this animation to explain the concept of area and its application in geometry.	Definition of a Triangle
Animated Math Clip Art--Triangles--Right Triangle Area 2	Animated Math Clip Art--Triangles--Right Triangle Area 2 Topic Triangles Description This animation illustrates another example of calculating the area of a right triangle. The animation reinforces the concept of using the base and height to determine the area, helping students to understand and apply the formula in various contexts. Using animated math clip art in teaching enhances student engagement and understanding by providing a clear and interactive learning experience. Teachers can use this animation to facilitate discussions about the concept of area and its applications.	Definition of a Triangle
Animated Math Clip Art--Triangles--Right Triangles 1	Animated Math Clip Art--Triangles--Right Triangles 1 Topic Triangles Description This animation depicts a right triangle, characterized by one 90-degree angle. The animation highlights the right angle, helping students to identify and understand the properties of right triangles. This visual representation is essential for recognizing right triangles and their applications in geometry. Animated math clip art is an effective tool for teaching geometric concepts, making them more engaging and comprehensible for students. Teachers can use this animation to discuss the properties and applications of right triangles.	Definition of a Triangle
Animated Math Clip Art--Triangles--Right Triangles 2	Animated Math Clip Art--Triangles--Right Triangles 2 Topic Triangles Description This animation provides another example of a right triangle, emphasizing the 90-degree angle. The animation helps students to visualize and understand the characteristics of right triangles, reinforcing their ability to identify these triangles in various contexts. Incorporating animated math clip art into lessons engages students and enhances their understanding of geometric concepts. Teachers can use this animation to encourage students to explore the properties and applications of right triangles.	Definition of a Triangle
Animated Math Clip Art--Triangles--The Sum of the Angles of a Triangle	Animated Math Clip Art--Triangles--The Sum of the Angles of a Triangle Topic Triangles Description This animation demonstrates the concept that the sum of the angles in a triangle is always 180 degrees. The animation visually shows how the angles add up to form a straight line, making it easier for students to understand this fundamental geometric principle. Animated math clip art provides a dynamic way to teach mathematical concepts, making them more engaging and understandable for students. Teachers can use this animation to explain the sum of angles in a triangle and its applications in geometry.	Definition of a Triangle
Animated Math Clip Art--Triangles--The Sum of the Angles of a Triangle 2	Animated Math Clip Art--Triangles--The Sum of the Angles of a Triangle 2 Topic Triangles Description This animation demonstrates the concept that the sum of the angles in a triangle is always 180 degrees. The visual representation shows how the angles combine to form a straight line, reinforcing the understanding of this fundamental geometric principle. Animated math clip art is an effective educational tool as it visually demonstrates mathematical concepts, making them more accessible and engaging for students. By using this animation, teachers can help students visualize and understand the theorem, facilitating a deeper comprehension of triangle properties.	Definition of a Triangle
Animated Math Clip Art--Triangles--Triangle Area 1	Animated Math Clip Art--Triangles--Triangle Area 1 Topic Triangles Description This animation illustrates how to calculate the area of a triangle using the formula 1/2 × base × height. The animation highlights the base and height, helping students understand the components needed to find the area of a triangle. Using animated math clip art enhances student engagement and understanding by providing a dynamic and interactive way to learn. Teachers can use this animation to encourage students to explore and apply the formula in various contexts. Teacher’s Script: "Watch how we calculate the area of this triangle. What do we need to know to find the area?"	Definition of a Triangle
Animated Math Clip Art--Triangles--Triangle Area 2	Animated Math Clip Art--Triangles--Triangle Area 2 Topic Triangles Description This animation provides another example of calculating the area of a triangle, reinforcing the use of the base and height in the formula 1/2 × base × height. The animation helps students visualize and understand how to apply this formula to determine the area. Incorporating animated math clip art into lessons engages students and enhances their understanding of mathematical concepts. Teachers can use this animation to facilitate discussions about the concept of area and its applications. Teacher’s Script: "Look at how we find the area of this triangle. How can we use this knowledge in different situations?"	Definition of a Triangle
Animated Math Clip Art--Triangles--Triangle Inequality 1	Animated Math Clip Art--Triangles--Triangle Inequality 1 Topic Triangles Description This animation illustrates the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. The animation visually demonstrates this principle, helping students to understand and apply it in geometric contexts. Animated math clip art provides a clear and engaging way to learn complex concepts. Teachers can use this animation to explain the Triangle Inequality Theorem and its applications in geometry.	Definition of a Triangle
Animated Math Clip Art--Triangles--Triangle Inequality 2	Animated Math Clip Art--Triangles--Triangle Inequality 2 Topic Triangles Description This animation provides another demonstration of the Triangle Inequality Theorem, reinforcing the concept that the sum of the lengths of any two sides must exceed the length of the third side. The animation helps students visualize and apply this theorem in various scenarios. Using animated math clip art in teaching enhances student engagement and understanding by providing a dynamic and interactive learning experience. Teachers can use this animation to encourage students to explore the properties and applications of the Triangle Inequality Theorem.	Definition of a Triangle
Animated Math Clip Art--Triangles--Triangle Perimeter 1	Animated Math Clip Art--Triangles--Triangle Perimeter 1 Topic Triangles Description This animation shows how to calculate the perimeter of a triangle by summing the lengths of its sides. The animation highlights each side, helping students understand the concept of perimeter and its calculation in triangles. Animated math clip art provides a dynamic way to teach mathematical concepts, making them more engaging and understandable for students. Teachers can use this animation to explain the concept of perimeter and its application in geometry. Teacher’s Script: "Watch how we calculate the perimeter of this triangle. What do we need to know to find the perimeter?"	Definition of a Triangle
Animated Math Clip Art--Triangles--Triangle Perimeter 2	Animated Math Clip Art--Triangles--Triangle Perimeter 2 Topic Triangles Description This animation provides another example of calculating the perimeter of a triangle, reinforcing the concept of summing the side lengths. The animation helps students visualize and understand how to determine the perimeter in different contexts. Incorporating animated math clip art into lessons engages students and enhances their understanding of geometric concepts. Teachers can use this animation to facilitate discussions about the concept of perimeter and its applications. Teacher’s Script: "Look at how we find the perimeter of this triangle. How can we use this knowledge in different situations?"	Definition of a Triangle
Closed Captioned Video: Circumcenter of a Triangle	Closed Captioned Video: Circumcenter of a Triangle In this TI Nspire tutorial, the Geometry window is used to construct a triangle and its circumcenter. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .	Geometric Constructions with Triangles
Closed Captioned Video: Circumscribing a Circle-Triangle	Closed Captioned Video: Circumscribing a Circle-Triangle In this TI Nspire tutorial, the Geometry window is used to circumscribe a circle about a triangle. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .	Geometric Constructions with Triangles
Closed Captioned Video: Geometry Applications: Triangles	Closed Captioned Video: Geometry Applications: Triangles 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.	Definition of a Triangle and Applications of Triangles
Closed Captioned Video: Geometry Applications: Triangles, 1	Closed Captioned Video: Geometry Applications: Triangles, Segment 1: Introduction 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.	Definition of a Triangle and Applications of Triangles
Closed Captioned Video: Geometry Applications: Triangles, 2	Closed Captioned Video: Geometry Applications: Triangles, Segment 2: 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.	Definition of a Triangle and Applications of Triangles
Closed Captioned Video: Geometry Applications: Triangles, 3	Closed Captioned Video: Geometry Applications: Triangles, Segment 3: 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.	Definition of a Triangle and Applications of Triangles
Closed Captioned Video: Orthocenter of a Triangle	Closed Captioned Video: Orthocenter of a Triangle In this TI Nspire tutorial the Geometry window is used to construct the orthocenter of a triangle. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. . This is part of a collection of closed captioned videos on various math topics. To see the complete collection of the videos, click on this link. Note: The download is Media4Math's guide to closed captioned videos. Related Resources To see additional resources on this topic, click on the Related Resources tab. Video Transcripts This video has a transcript available. To see the complete collection of video transcripts, click on this link.	Geometric Constructions with Triangles
Definition--Circle Concepts--Circle Inscribed in a Triangle	Circle Inscribed in a Triangle Topic Circles Definition An inscribed circle in a triangle is tangent to each of the triangle's sides.	Definition of a Circle
Definition--Circle Concepts--Circumcenter of Triangle	Circumcenter of Triangle Topic Circles Definition The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect, equidistant from the vertices.	Definition of a Circle
Definition--Circle Concepts--Incenter of a Triangle	Incenter of a Triangle Topic Circles Definition The incenter of a triangle is the point where the angle bisectors intersect, equidistant from the sides.	Definition of a Circle
Definition--Circle Concepts--Triangle Inscribed in a Circle	Triangle Inscribed in a Circle Topic Circles Definition A triangle inscribed in a circle has its vertices on the circle.	Definition of a Circle
Definition--Geometry Basics--Circle Inscribed In a Triangle	Circle Inscribed In a Triangle Topic Geometry Basics Definition A circle that is tangent to all three sides of a triangle. Description A circle inscribed in a triangle is a circle that is tangent to all three sides of the triangle. This concept is important in understanding the properties of triangles and their relationship with circles. For example, the radius of the inscribed circle can be used to calculate the area of the triangle using the formula Area = 1/2 × perimeter × radius. Understanding inscribed circles helps in solving problems related to triangle geometry and optimization.	Definition of a Circle
Definition--Geometry Basics--Circumcenter of a Triangle	Circumcenter of a Triangle Topic Geometry Basics Definition The point where the perpendicular bisectors of a triangle intersect. Description The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. This point is equidistant from all three vertices of the triangle. Understanding the circumcenter is important in solving problems related to triangle geometry and circle properties. For example, the circumcenter is the center of the circumscribed circle that passes through all three vertices of the triangle.	Definition of a Circle
Definition--Geometry Basics--Incenter of a Triangle	Incenter of a Triangle Topic Geometry Basics Definition The point where the angle bisectors of a triangle intersect.	Definition of a Circle
Definition--Geometry Basics--Inscribed Triangle	Inscribed Triangle Topic Geometry Basics Definition A triangle drawn within another triangle, where each vertex touches the circumcircle. Description The inscribed triangle illustrates essential relationships between triangles and circles. Understanding this concept involves recognizing properties such as area calculations involving the circumcircle and relationships among various elements of triangles. The area can be found using the formula related to the circumradius and semi-perimeter, enhancing problem-solving skills and applying real-world considerations such as construction and design.	Definition of a Circle

Illustrative Math Alignment: Grade 7 Unit 7

Angles, Triangles, and Prisms

Lesson 8: Triangles with 3 Common Measures

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