Massachusetts Department of Education
Similarity through Transformations
Create the ultimate miniature golf course. The 93-page model curriculum unit from the Massachusetts Department of Elementary and Secondary Education contains nine lessons on understanding similarity in terms of both Euclidean geometry...
Curated OER
Similarity and Dilations - Discover Properties of Similar Figures
Learners investigate properties of similar figures. In this properties of similar figures lesson, pupils construct similar figures using Cabri Jr. They dilate their figure to create a similar one, and discuss the relationships between...
CK-12 Foundation
Lengths of Sides in Isosceles Right Triangles: Paper Football
Fuse sports and geometry by having your class create paper footballs—that are actually isosceles right triangles! Scholars use an interactive to create an isosceles right triangle to model a paper football. From the information in the...
West Contra Costa Unified School District
Congruent and Similar Polygons
What's similar about congruent and similar polygons? Young mathematicians first measure the side lengths and angles of given figures. They use these measurements to determine relationships between side lengths and angles of congruent and...
CK-12 Foundation
Pythagorean Theorem to Classify Triangles: Missing Angles
Learn to use the Pythagorean Theorem with non-right triangles. Pupils use the interactive to discover the relationship between the lengths of sides for acute and obtuse triangles. They compare the squares of the sides of the triangles to...
CK-12 Foundation
Lengths of Triangle Sides Using the Pythagorean Theorem: Find the Missing Side
What is the relationship between the sides of a right triangle? Learners use an interactive to create models of right triangles and view the relationship between the lengths of the sides. They finish by using the Pythagorean Theorem to...
CK-12 Foundation
Relationships of Sides in 30-60-90 Right Triangles: Truck on a Mountain Road
Determine the change in elevation on a mountain road. Individuals use the interactive to simulate a truck driving up a mountain road with a 30-degree incline. They determine missing sides of a 30-60 right triangle to find horizontal and...
CK-12 Foundation
Alternate Formula for the Area of a Triangle: Alternate Area of a Triangle
It's always nice to have a plan B. Pupils investigate an alternate formula for the area of a triangle that uses sine. A set of challenge questions shows how the new formula relates to the well-known formula of (1/2)bh.
CK-12 Foundation
Pascal's Triangle: Pyramid Blocks
Build a pyramid of sums. An interactive presents the first five rows of Pascal's Triangle as a pyramid. Pupils match missing entries in the pyramid and continue the pattern to determine entries of other rows. The learners use the entries...
Virginia Department of Education
Special Right Triangles and Right Triangle Trigonometry
Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...
EngageNY
Similarity
Use the coordinate plane to show two figures are similar. The lesson incorporates congruence transformations and dilations to move a figure on to another figure. Pupils determine that if a similarity transformation exists between two...
Curated OER
What Is Hyperbolic Geometry?
Ninth graders discuss the concept of hyperbolic geometry. They complete Internet geometry activities and write essays comparing and contrasting hyperbolic geometry to Euclidean geometry.
Curated OER
Exploring Polygons and The Greedy Triangle
Excellent lesson! Anne Linehane's geometry story, The Greedy Triangle, offers an opportunity to practice forming various types of polygons with your learners. Using elastic bands (or Chinese jump ropes), partners form the various shapes...
Curated OER
Tennis Triangle
Learners calculate the height of a tree or flagpole. They measure the shadow of the tree or flagpole and the length of a shadow of a meterstick. Using similar triangles, calculate the heigh. Devise two additional ways in which to measure...
EngageNY
Between-Figure and Within-Figure Ratios
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...
Illustrative Mathematics
Equal Area Triangles on the Same Base II
A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...
EngageNY
Are All Parabolas Similar?
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.
Mathematics Assessment Project
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.
Illustrative Mathematics
Coordinates of Equilateral Triangles
Can it be constructed? The task poses the question whether it is possible to have an equilateral triangle with its vertices located at integer coordinates. Pupils work with their knowledge of trigonometric ratios and the Pythagorean...
Curated OER
Similar Figures
In this geometry worksheet students explore similar polygons and determine measure of missing sides and angles. Students use indirect measurement with similar triangles and determine the area and volume of similar figures. The seven page...
Mathematics Assessment Project
Hopewell Geometry
Right triangles from 2,000 years ago? Learners investigate different right triangles found in the earthworks of the Hopewell people, a Native American culture that populated the United States from 200BC to AD 500. Learners apply concepts...
Curated OER
Countdown Challenge: Similarity
In this similarity activity, students use similar rectangles to find the length of a diagonal. They use symbols and write paragraphs to explain the problem. This one-page activity contains one similar problem with 13 related questions.
El Paso Community College
Geometry Definitions
Geometry is full of shapes, figures, and corresponding things here and there. The guide shares all of the key pieces of geometric information in a nicely color-coded and labeled sheet.
Curated OER
Mt. Whitney to Death Valley
This is an intriguing problem that brings together real-world data, technology, and mathematical problem solving. If visibility wasn't an issue, could you see from the highest point in the lower 48 states, Mt. Whitney, to the lowest...