CSI Investigation of Congruence and Similarity

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...

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.

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...

Use the natural logarithm to simplify differentiation. The 22nd resource in a series of 31 provides an example of a problem that would be best differentiated by using logarithms. The presenter takes the natural logarithm of both sides....

It's implied that implicit differentiation is important. Viewers of an engaging video learn the process of implicit differentiation. After watching several examples, they see how to apply implicit differentiation to find the vertical and...

Explicitly explain how to use implicit differentiation. Using a trigonometric function defined using y and x, the resource works through an example of implicit differentiation to explain the process. The 19th video in a 31-part series...

Find the square of the scale factor. A component of a large playlist on geometry discusses the ratios of the perimeters and areas of two similar polygons. The resource shows examples in finding the ratios that lead to a pattern.

Despite what you thought, you can differentiate between continuity and differentiability. Using a short lesson, pupils learn how differentiability and continuity relate to each other. It provides three descriptions of when a function is...

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...

The legend of a wise man who asks a king for rice as a reward presents a context to study exponential solutions to differential equations. Pupils move quantities of rice to a chessboard and calculate the amount of rice for each day. To...