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...

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...

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...

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...

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.

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....

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...

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...

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...

Two triangles are displayed on a coordinate plane. Youngsters apply a reflection and a translation to demonstrate their congruence. This exercise makes a terrific tool for teaching these concepts, or a way to assess learning.

Congruence and similarity apply to functions as well as polygons. Learners examine the effects of transformations on the shape of parabolas. They determine the transformation(s) that produce similar and congruent functions.

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...

Looking for a different approach to triangle congruence criteria? Employ transformations to determine congruent triangles. Learners list the transformations required to map one triangle to the next. They learn to identify congruence...

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...

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...

Transform your pupils into mathematicians as they learn to prove the popular Pythagorean Theorem. The 16th lesson in the series of 25 continues by teaching learners how to develop a proof. It shows how to prove the Pythagorean Theorem...

There is more to congruency than just looking similar. Learn the difference and calculate the matching angles and sides to prove the congruence between figures. Lesson has step-by-step slides and follows with an assessment. 

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...

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. 

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...

Who needs a plan — let trigonometry protect you! Pupils determine the angle of an approaching enemy to a village wall. The scholars determine the exact value of trigonometric functions for the angle. Class members use trigonometry to...

Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...

Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...