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Classifying Triangles based on angle measures

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Classifying Triangles based on angle measures

Students solve for missing interior angles in triangles.  Triangles are on individual cards.  Students determine appropriate "angle" and "side" terms (acute, obtuse, right, scalene, isosceles, equilateral) and place the triangle cards into the table.  Opportunity to address why certain descriptions are impossible (such as an equilateral right triangle) and why it's impossible to have a triangle with more than 1 obtuse angle.

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• Unit 2

Dilate Triangles

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Dilate Triangles

Students will dilate triangles using a compass.  Students will analyze the relationship between angle measures and segment/side lengths of pre-images and images.

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• Unit 3

#### Similarity and Proof

Example Proofs of the Pythagorean Theorem

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Example Proofs of the Pythagorean Theorem

Website that models different proofs of the Pythagorean theorem, with diagrams.

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• Unit 4

#### Right Triangle Trigonometry

Finding the Height of Your School

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Finding the Height of Your School

Using right triangle trigonometry, students will be able to find the height of the school building.

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• Unit 4

#### Right Triangle Trigonometry

Finding Triangle Coordinates

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Finding Triangle Coordinates

The purpose of this task is to use similar triangles in order to study the coordinates of points which divide a line segment in a given ratio. These coordinates can be calculated directly but the method employed here not only allows us to find the coordinates of the desired points but also to construct them (with straightedge and compass).

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• Unit 3

#### Similarity and Proof

GeoGebra Slider AA Similar Triangles

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GeoGebra Slider AA Similar Triangles

Slider that shows 2 similar triangles formed by parallel lines and 2 transversals.  The focus is on the vertical angles and the alternate interior angle pairs.

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• Unit 3

#### Similarity and Proof

GeoGebra Slider that shows the sum of the interior angles of a triangle equal 180 degrees

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GeoGebra Slider that shows the sum of the interior angles of a triangle equal 180 degrees

Slider shows that all 3 angles in a triangle add to 180 degrees.  Can be used to classify triangles as acute, obtuse, right, scalene, isosceles, equilateral.  Can be used to analyze angle side relationships.

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• Unit 2

Inscribing and Circumscribing Right Triangles

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Inscribing and Circumscribing Right Triangles

A Classroom Challenge (aka formative assessment lesson) is a classroom-ready lesson that supports formative assessment. The lesson’s approach first allows students to demonstrate their prior understandings and abilities in employing the mathematical practices, and then involves students in resolving their own difficulties and misconceptions through structured discussion.

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• Unit 7

#### Circles

Overlapping Triangles

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Overlapping Triangles

Students will be able to connect diagrams containing overlapping triangles to diagrams showing those triangles separated.

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• Unit 2

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Lesson Plan that outlines how to facilitate students proving the Pythagorean theorem.

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• Unit 4

#### Right Triangle Trigonometry

Right Triangles Inscribed in Circles 1

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Right Triangles Inscribed in Circles 1

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle with one side of the triangle a diameter: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.

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• Unit 7

#### Circles

Right Triangles Inscribed in Circles 2

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Right Triangles Inscribed in Circles 2

The result here complements the fact, presented in the task ''Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle.

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• Unit 7
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