EngageNY
Conditions for a Unique Triangle—Three Sides and Two Sides and the Included Angle
Building on the previous activity in the 29-part series, the ninth activity asks individuals to construct a triangle given specific criteria. First, they are given three specific side lengths, followed by two sides and the included...
Texas Instruments
Identifying a Triangle by its Sides and Angles
Identify triangles by their angle measures and side lengths by looking at and measuring angle measures and side lengths. Use Cabri Jr. to construct various triangles, then manipulate the construction to create the 6 types of triangles,...
Captain Planet Foundation
Frog Garden Party! Toads and Triangles in the Math Garden
It's frog party time! With frog banners, frog juice, and a triangle hunt, your garden party is sure to be both entertaining and educational. The activity connects geometry, earth science, and delicious snacks to teach kids about...
Curated OER
Two Triangles' Area
Need an activity for teaching the Pythagorean Theorem? Geometry juniors apply the Pythagorean theorem to two triangles to determine a final calculation.
EngageNY
The Angle-Angle (AA) Criterion for Two Triangles to Be Similar
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...
EngageNY
An Area Formula for Triangles
Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....
Illustrative Mathematics
Right Triangles Inscribed in Circles II
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...
Virginia Department of Education
Congruent Triangles
Is this enough to show the two triangles are congruent? Small groups work through different combinations of constructing triangles from congruent parts to determine which combinations create only congruent triangles. Participants use the...
Virginia Department of Education
Similar Triangles
Pupils work in pairs to investigate what it takes to prove that two triangles are similar. They work through various shortcuts to find which are enough to show a similarity relationship between the triangles. Small groups work with the...
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
Drawing Triangles
Create concrete examples of triangle congruence for your classes. The eighth installment of the 29-part module sets the stage for studying triangle congruence. Given a set of criteria, math scholars use constructions to build a specific...
EngageNY
Unique Triangles—Two Sides and a Non-Included Angle
Construct an understanding of triangle congruence through a visual analysis. Young scholars find that given two sides and a non-included angle, sometimes two possible triangles are produced. Their analysis shows that if the non-included...
EngageNY
Special Lines in Triangles (part 1)
Allow your pupils to become the mathematicians! Individuals explore the properties of a midsegment of a triangle through construction and measurement. Once they figure out the properties, learners use them to draw conclusions.
EngageNY
Special Lines in Triangles (part 2)
Medians, midsegments, altitudes, oh my! Pupils study the properties of the median of a triangle, initially examining a proof utilizing midsegments to determine the length ratio of a median. They then use the information to find missing...
EngageNY
Special Triangles and the Unit Circle
Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value...
Illustrative Mathematics
Similar Triangles
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...
Curated OER
Circumscribing a Circle About a Triangle
Pupils circumscribe a circle about a triangle. They construct a triangle using Cabri Jr and then circumscribe it. They then use knowledge of perpendicular bisectors and circumcenters to locate the center of the circle and then...
EngageNY
Congruence Criteria for Triangles—ASA and SSS
How do you know if a pair of triangles are congruent? Use the lesson to help class members become comfortable identifying the congruence criteria. They begin with an exploration of ASA and SSS criteria through transformations and...
EngageNY
Construct an Equilateral Triangle (part 2)
Triangles, triangles, and more triangles! In this second installment of a 36-part series, your young mathematicians explore two increasingly challenging constructions, requiring them to develop a way to construct three triangles that...
EngageNY
The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
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...
EngageNY
Construct an Equilateral Triangle (part 1)
Drawing circles isn't the only thing compasses are good for. In this first installment of a 36-part series, high schoolers learn how to draw equilateral triangles by investigating real-world situations, such as finding the location of a...
Curated OER
The Greedy Triangle-Intro to Geometric Shapes
In this geometry lesson, learners read The Greedy Triangle and use geoboards to construct geometric shapes. They identify the number of sides and angles each shape has.
Curated OER
Finding the Area of an Equilateral Triangle
The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle...
Illustrative Mathematics
Right Triangles Inscribed in Circles I
One of the basic properties of inscribed angles gets a triangle proof treatment in a short but detailed exercise. Leading directions take the learner through identifying characteristics of a circle and how they relate to angles and...