What do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find...

Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...

After reviewing characteristics of seven types of triangles, young geometers discover how to find the missing angle of a triangle. Then, they practice identifying triangles, find missing angles, and find missing side lengths of...

Introduce your classes to a new world of mathematics. Pupils learn to call trigonometric ratios by their given names: sine, cosine, and tangent. They find ratios and use known ratios to discover missing sides of similar...

Given a pair of parallel lines and a triangle in between, geometers prove that the sum of the interior angles is 180 degrees. This quick quest can be used as a pop quiz or exit ticket for your geometry class.

What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...

Discover how triangles are congruent based on their sides, angles, and proportionality. Learners explore the ways to determine similarity at their own pace, and then they practice afterwards with an assessment. 

Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once...

Amaze your classes with the ability to find side lengths of triangles immediately — they'll all want to know your trick! Learners use the Pythagorean Theorem and special right triangle relationships to find missing side lengths.

Start the exploration of trigonometry off right! Pupils build on their understanding of similarity in this instructional activity that introduces the three trigonometric ratios. They first learn to identify opposite and adjacent...

First angle measures, now segment lengths. High schoolers first measure segments formed by secants that intersect interior to a circle, secants that intersect exterior to a circle, and a secant and a tangent that intersect exterior to a...

Observe the change in the trigonometric ratios as angles vary. An interactive provides the values of trigonometric ratios for both acute angles in a right triangle. Pupils create a right triangle to match given criteria and find the...

Full of problems with polygons, angles, lines, and triangles, your learners get a multi-page packet that provides all they need to know. It contains many of the standard problem types as well as some more challenging questions. 

Increase the level of assessment rigor with the test of performance tasks. Topics include similar triangles, trigonometric ratios, Law of Sines, Law of Cosines, and trigonometric problem solving. 

Does the space shuttle have an odometer? Maybe, but all that is needed to determine the distance to the moon is a little geometry! The lesson asks scholars to sketch the relationship of the Earth and moon using shadows of an eclipse....

Investigate how similar and congruent figures compare. Learners understand congruent figures have congruent sides and angles, but similar figures only have congruent angles — their sides are proportional. After learning the...

What's the point of looking at triangles when trying to draw parallelograms? Given three non-collinear points, pupils determine and justify all possible points that would create a parallelogram. They then analyze the four triangles that...

Playing with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...

Just what does it take to show two rhombuses are similar? The assessment task asks pupils to develop an argument to show that given quadrilaterals are rhombuses. Class members also use their knowledge of similar triangles to show two...

The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...

What does similarity have to do with the Pythagorean Theorem? The activity steps through the proof of the Pythagorean Theorem by using similar triangles. Next, the teacher leads a discussion of the proof and follows it by an animated...

Fuse sports and geometry by having your class create paper footballs—that are actually isosceles right triangles! Scholars use an interactive to create an isosceles right triangle to model a paper football. From the information in the...

Learn to use the Pythagorean Theorem with non-right triangles. Pupils use the interactive to discover the relationship between the lengths of sides for acute and obtuse triangles. They compare the squares of the sides of the triangles to...

What is the relationship between the sides of a right triangle? Learners use an interactive to create models of right triangles and view the relationship between the lengths of the sides. They finish by using the Pythagorean Theorem to...