Are they similar? The lesson provides an explanation of the angle-angle criterion for triangle similarity. Several problems allow the class to determine whether the two triangles with the given angle measures are similar or not. 

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...

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...

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...

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...

Apply the concept of similar triangles to design a space in a room. Scholars use similar triangles to determine how a spotlight reflects from a mirror. After drawing the path of the spotlight, individuals find the smallest possible width...

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...

So many times the characteristics of triangles are presented as a vocabulary-type of lesson, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a...

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...

How do you find the lengths of items that cannot be directly measured? The 13th installment in a series of 16 has pupils use the similarity content learned in an earlier resource to solve real-world problems. Class members determine...

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...

Try to figure out what happens with shadows as a person moves between two light sources. A formative assessment lesson has individuals work on an assessment task based on similar triangles, then groups them based on their...

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. 

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.

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...

Does the symmetry and transitive property apply to similarity? The 10th segment in a series of 16 presents the class with a group of explorations. The explorations have pairs show that similarity is both symmetrical and transitive....

Sometimes the solution is all a matter of perspective. The short assessment task presents a problem to pupils that requires them to make sense of a diagram. Once learners see two similar triangles, the rest of the solution is solving a...

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...

Show more than one way to prove similarity. Scholars learn three different methods to show two triangles are similar, Angle-Angle, Side-Side-Side, and Side-Angle-Side. Pupils practice applying these methods to determine whether two given...

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...

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 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...