University of Utah
Geometry: Angles, Triangles, and Distance
The Pythagorean Theorem is a staple of middle school geometry. Scholars first investigate angle relationships, both in triangles and in parallel lines with a transversal, before proving and applying the Pythagorean Theorem.
EngageNY
Construct an Equilateral Triangle (part 2)
Triangles, triangles, and more triangles! In this second installment of a 36-part series, your young mathematicians explore two increasingly challenging constructions, requiring them to develop a way to construct three triangles that...
Mathematics Assessment Project
Solving Problems with Circles and Triangles
After completing a task involving examining the ratio of areas of triangles and circles in a given figure, scholars examine sample responses to identify other strategies they could use to solve the problem.
EngageNY
Triangle Congruency Proofs (part 2)
Looking to challenge your young scholars that have mastered basic triangle congruence proofs? A collection of proofs employ previously learned definitions, theorems, and properties. Pupils draw on their past experiences with proofs...
Mathematics Assessment Project
Circles in Triangles
Circles, and triangles, and tangents, oh my! In the assessment task, learners first answer questions leading to the radius of an inscribed circle for a given right triangle. They then use the result to independently determine the...
Education Development Center
Similar Triangles
Model geometric concepts through a hands-on approach. Learners apply similar triangle relationships to solve for an unknown side length. Before they find the solution, they describe the transformation to help identify corresponding sides.
Alabama Learning Exchange
Triangle Area: No Height? Use the Sine
No height? No problem! Learners use their knowledge and a little help from GeoGebra to develop the Law of Sines formula. The Law of Sines helps to determine the height of triangles to calculate the area.
Mathematics Assessment Project
Inscribing and Circumscribing Right Triangles
High schoolers attempt an assessment task requiring them to find the radii of inscribed and circumscribed circles of a right triangle with given dimensions. They then evaluate provided sample responses to consider how to improve...
EngageNY
Triangle Congruency Proofs (part 1)
Can they put it all together? Ninth graders apply what they know about proofs and triangle congruence to complete these proofs. These proofs go beyond the basic triangle congruence proofs and use various properties, theorems, and...
Illustrative Mathematics
Equal Area Triangles on the Same Base II
A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...
West Contra Costa Unified School District
Investigating Special Right Triangles
Scholars first investigate relationships in the side lengths of 30°-60°-90° triangles and 45°-45°-90° triangles. This knowledge then helps them solve problems later in the lesson plan about special right triangles.
EngageNY
Construct an Equilateral Triangle (part 1)
Drawing circles isn't the only thing compasses are good for. In this first installment of a 36-part series, high schoolers learn how to draw equilateral triangles by investigating real-world situations, such as finding the location of a...
EngageNY
Special Triangles and the Unit Circle
Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value...
Illustrative Mathematics
Coordinates of Equilateral Triangles
Can it be constructed? The task poses the question whether it is possible to have an equilateral triangle with its vertices located at integer coordinates. Pupils work with their knowledge of trigonometric ratios and the Pythagorean...
CPALMS
2D Rotations of Triangles
Where does the line of rotation need to be to get a cone? Pupils respond to three questions involving rotating a right triangle about different lines. The scholars describe the solid created along with providing details about its...
Concord Consortium
In a Triangle
What's in a triangle? Just 180 degrees worth of angles! Young learners use given angle relationships in a triangle to write an algebraic representation. Using a system of equations, they simplify the equation to a linear representation.
GeoGebra
Triangle Dilations
Stretch the class' knowledge of dilations. With the aid of the rubber band stretcher tool, learners perform dilations. They dilate the triangle by a whole number scale and a fractional scale from two centers of dilation.
Curated OER
Constructions Triangles
Learners explore the difference between a construction and a drawing. They focus on various ways to construct different types of triangles. The lesson is an application of Cabri Jr. and reinforces the difference between a constructions...
Curated OER
Triangles
In this triangles instructional activity, 10th graders solve 3 extensive informal geometry problems that involve triangles. First, they sketch a triangle, selecting 3 of the sides and constructing 3 midpoints. Students then draw each of...
Curated OER
Triangle Problems-Base, Height, and Area
For this geometry worksheet, 10th graders find the base, height, or area of a triangle. The one page interactive worksheet contains ten questions. Answers and hints are included.
Curated OER
Learning Triangles
In this triangles instructional activity, students recognize triangles. Students complete the instructional activity by practicing drawing triangles and recognizing triangles in a picture.
Curated OER
Circumscribing a Circle About a Triangle
Pupils circumscribe a circle about a triangle. They construct a triangle using Cabri Jr and then circumscribe it. They then use knowledge of perpendicular bisectors and circumcenters to locate the center of the circle and then...
Curated OER
Investigating Segments in a Triangle
Pupils investigate segments in a triangle by constructing a triangle using Cabri Jr. They construct segments within the triangle that lie on the midpoints of the triangle's sides. Learners then compare the slope of base of the triangle...
Curated OER
Measuring Angles in a Triangle
High schoolers investigate the sum of the measures of the angles of a triangle. They draw a triangle and measure the interior angles. Using Cabri Jr., learners find the sum of the measures of the interior angles. The lesson provides an...
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