Determine whether two triangles are similar. The lesson presents opportunities for pupils to find the criterion needed to show that two triangles are similar. Scholars use the definition of similarity to find any missing side...

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...

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...

Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...

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...

Go from one side length to any other side length with special right triangles. Individuals use the interactive to investigate the ratio of sides in 45-45 and 30-60 right triangles. Scholars make generalizations about the types of special...

Tie the unit together and see concepts click in your young mathematicians' minds. Scholars apply the properties of similar triangles to find heights of objects. They concentrate on the proportions built with known measures and solve to...

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.

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...

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...

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...

Use some similar problems to find side lengths. Pupils learn the definition of similar figures and how it relates to corresponding angles and sides. Using the definition, individuals calculate the lengths of missing sides and practice...

Learners take on the role of astronomers, calculating conditions necessary for a total solar eclipse. Concepts of similar triangles and properties of circles come together as pupils create ratios and use real measurements in determining...

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...

Does doubling mean everything doubles? Learners adjust the scale factor between two rectangles. Using the calculated measurements, pupils investigate the ratios between the lengths, perimeters, and areas of the rectangles.

Take a similar approach to three dimensions. Pupils develop the relationship between areas of similar objects and see how they relate to the ratio of the sides. Building upon area formulas, small groups put together volume formulas for...

Climb the ladder to trigonometry. The interactive introduces trigonometric ratios and finding lengths of sides of right triangles created by a ladder and a building. Learners use the interactive to create triangles by moving the top of...

Ancient Egyptians sure knew their trigonometry! Pupils learn how the pyramid architects applied right triangle trigonometry. When comparing the Pythagorean theorem to the trigonometric ratios, they learn an important connection that...

Compare iPad and HDTV aspect ratios. Individuals use the interactive to determine whether the measurements of screens represent a Pythagorean triple. The pupils determine what changes are needed to make a Pythagorean triple.

Determine the length of a falling ladder. Pupils use an interactive to find the angle a ladder makes with the floor after it falls to answer questions. The scholars use the triangle formed in the interactive to determine values of...

As they investigate scaling figures and calculate the resulting areas, groups determine the area of similar figures. They continue to investigate the results when the vertical and horizontal scales are not equal. 

Is it bigger, or is it smaller—or maybe it's the same size? Individuals learn to describe enlargements and reductions and quantify the result. Lesson five in the series connects the creation of a dilated image to the result. Pupils...