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EngageNY

#### EngageNY Geometry Module 2: Similarity, Proof, and Trigonometry

The Geometry Module 2: Similarity, Proof, and Trigonometry collection includes 36 lessons that are divided into five topics: Scale Drawings, Dilations, Similarity and Dilations, Applying Similarity to Right Triangles, and Trigonometry....

Lesson Planet

#### Analyzing Congruence Proofs

Looking at numerous examples of triangles, each with different properties, geometers develop their understanding of congruency. They use the notation of a counter-example to disprove certain conjectures and prove geometric theorems and...

Lesson Planet

#### The Puppy’s Empire

Dogs can't do math ... but people sure can! A set of five lessons has scholars apply math concepts to solve problems related to buying a new dog, such as designing a fence and a dog house, estimating how large the dog will become, and...

Lesson Planet

#### Module 4: Similarity and Right Triangle Trigonometry

Right you are to use a great resource. Starting with a lesson on dilations, scholars learn about similarity transformations and similar triangles. They use the knowledge to develop an understanding of right triangle trigonometry in later...

Lesson Planet

#### Triangle Proportionality: Lesson

Look at proportionality from a parallel perspective. A section of an expansive geometry playlist introduces the Triangle Proportionality Theorem. Using the theorem, the video shows how to determine missing measurements in triangles.

Lesson Planet

#### Parametric Equations and a Heart

Trigonometry, art, and Valentine's Day come together in a creative activity about parametric equations. Learners calculate several equations before graphing them either by hand, on a graphic calculator, or Excel spreadsheet to curve...

Lesson Planet

#### Squaring the Triangle

Teach budding mathematicians how to square a triangle with an interactive that shows a graphical proof of the Pythagorean Theorem. Pupils alter the lengths of the legs using sliders. Using the inputted lengths, the applet displays the...

Lesson Planet

#### Triangle Proportionality Theorem

Parallel lines through triangles result in a special proportion. Scholars prove the triangle proportionality theorem in a great lesson. The resource makes use of angle relationships and the similarity criteria to build on their geometry...

Lesson Planet

#### Pythagorean Theorem Proof

We all know the Pythagorean Theorem, but why does it hold for all right triangles? Scholars first show the similarity of triangles when an altitude is drawn on the hypotenuse of a right triangle. Using the similar triangles, they prove...

Lesson Planet

#### Geometric Mean Proof

Mean is an average, but what is the geometric mean of two line segments? Scholars prove that the altitude to the hypotenuse is the geometric mean of the two parts of the hypotenuse. But first, they must explain why the two triangles...

Lesson Planet

#### Converse of the Triangle Proportionality Theorem

They say the proof is in the pudding ... hopefully, in this case, the theorem isn't in there as well! Learners tackle the task of explaining the relationships between segments within a triangle. The assessment is designed to demonstrate...

Lesson Planet

#### Pythagorean Theorem

Investigate the meaning of the Pythagorean Theorem through modeling. After comparing the area of the square of each side, individuals cut triangles and squares to facilitate the comparison.

Lesson Planet

#### The Pythagorean Relationship

Add up areas of squares to discover the pythagorean relationship. Small groups create right triangles with squares along each side. They calculate the areas of each square and notice the relationship. Groups construct other types of...

Lesson Planet

#### Modeling Motion: Rolling Cups

Connect the size of a rolling cup to the size of circle it makes. Pupils view videos of cups of different sizes rolling in a circle. Using the videos and additional data, they attempt to determine a relationship between cup measurements...

Lesson Planet

#### Deducting Relationships: Floodlight Shadows

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 assessment...

Lesson Planet

#### Evaluating Statements About Length and Area

Class members complete an assessment task by identifying whether statements about triangles and quadrilaterals are always true, sometimes true, or never true. They then participate in a sorting activity with the same objective.

Lesson Planet

#### Solving Problems with Circles and Triangles

After completing a task involving examining the ratio of areas of triangles and circles in a given figure, scholars examine sample responses to identify other strategies they could use to solve the problem.

Lesson Planet

#### Pythagorean Theorem Proofs

Your class knows the Pythagorean Theorem, but can they prove it? A series of three videos shows two proofs of the Pythagorean Theorem and use it to classify triangles.

Lesson Planet

#### Elementary Geometry

Your class may believe that geometry is a trial, but they don't know how right they are. A thorough math lesson combines the laws of logic with the laws of geometry. As high schoolers review the work of historical mathematicians and the...

EngageNY

#### How Do Dilations Map Angles?

The key to understanding is making connections. Scholars explore angle dilations using properties of parallel lines. At completion, pupils prove that angles of a dilation preserve their original measure.

EngageNY

#### Dilations as Transformations of the Plane

Compare and contrast the four types of transformations through constructions! Individuals are expected to construct the each of the different transformations. Although meant for a review, these examples are excellent for initial...

EngageNY

#### Making Scale Drawings Using the Parallel Method

How many ways can you create a dilation? Many! Individuals strengthen their understanding of dilations by using various methods to create them. The new technique builds on pupils' understanding of the ratio method. Using the ratio,...

EngageNY

#### Scale Drawings

Are you searching for a purpose for geometric constructions? Use an engaging approach to explore dilations. Scholars create dilations using a construction method of their choice. As they build their constructed dilation, they strengthen...

EngageNY

#### End-of-Module Assessment Task - Geometry (module 2)

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.