EngageNY
Triangle Congruency Proofs (part 1)
Can they put it all together? Ninth graders apply what they know about proofs and triangle congruence to complete these proofs. These proofs go beyond the basic triangle congruence proofs and use various properties, theorems, and...
EngageNY
Base Angles of Isosceles Triangles
Build confidence in proofs by proving a known property. Pupils explore two approaches to proving base angles of isosceles triangles are congruent: transformations and SAS. They then apply their understanding of the proof to more complex...
EngageNY
More on the Angles of a Triangle
Angles and triangles: they're all connected. Uncover the connections between angles in triangles. Scholars learn how to find both exterior and interior angle measures in triangles. The lesson emphasizes the vocabulary related to these...
Mathematics Assessment Project
Inscribing and Circumscribing Right Triangles
High schoolers attempt an assessment task requiring them to find the radii of inscribed and circumscribed circles of a right triangle with given dimensions. They then evaluate provided sample responses to consider how to improve their...
Curated OER
Exploring the Centroid of a Triangle
Pupils examine the centroid of a triangle as they use Cabri Jr. to construct a triangle and its medians. The dynamic nature of the software allows learners to measure the lengths of the segments in the triangle and conjecture and verify...
EngageNY
Definition and Properties of Volume
Lead a discussion on the similarities between the properties of area and the properties of volume. Using upper and lower approximations, pupils arrive at the formula for the volume of a general cylinder.
Curated OER
Which Triangles are Right
Students apply properties of right triangles to solve problems. In this geometry lesson, students identify axioms and theorems using examples.
Curated OER
What are the Kinds of Triangles?
Fifth graders classify triangles. In this triangle lesson, 5th graders learn about the characteristics that make up a triangle. They are instructed through video, PowerPoint slides, and teacher-led demonstrations.
Illustrative Mathematics
Placing a Fire Hydrant
Triangle centers and the segments that create them easily become an exercise in memorization, without the help of engaging applications like this lesson. Here the class investigates the measure of center that is equidistant to the three...
Illustrative Mathematics
Are They Similar?
Learners separate things that just appear similar from those that are actually similar. A diagram of triangles is given, and then a variety of geometric characteristics changed and the similarity of the triangles analyzed. Because the...
EngageNY
Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
EngageNY
Informal Proof of AA Criterion for Similarity
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...
Curated OER
Constructions Triangles
Learners explore the difference between a construction and a drawing. They focus on various ways to construct different types of triangles. The instructional activity is an application of Cabri Jr. and reinforces the difference between a...
Curated OER
Exploring the Circumcenter of a Triangle
Students construct the circumcenter of a triangle. In this constructing the circumcenter of a triangle lesson, students construct a triangle using Cabri Jr. Students draw perpendicular bisectors of the sides of the triangle. Students...
Curated OER
Exploring the Orthocenter of a Triangle
Young mathematicians explore the concept of triangles as they construct altitudes of triangles to find the orthocenter. Learners construct their triangles using Cabri Jr. on their graphing calculators and find that the altitudes of a...
Curated OER
Triangle Island
Students calculate the altitude of triangles. In the web based lesson, students explore the interior distance from a given point in a polygon to its side. They compute the sum of these lengths. Students read life application problems...
Curated OER
Measuring Angles in a Triangle
High schoolers investigate the sum of the measures of the angles of a triangle. They draw a triangle and measure the interior angles. Using Cabri Jr., learners find the sum of the measures of the interior angles. The lesson provides an...
Curated OER
How many isosceles Triangles Can You Find?
Fifth graders solve problems while examining a variety of isosceles triangles. For this isosceles triangle lesson, 5th graders examine shapes to find their characteristics. Students pay particular attention to the characteristics of...
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...
Curated OER
Congruent Triangles
Learners explore the concept of congruent triangles. In this congruent triangles lesson, students use Cabri Jr. to construct two congruent triangles using circles. Learners determine if the two triangles are congruent by using the SSS,...
Curated OER
Triangle Classificaition with Geometer's Sketchpad.
Students use Geometer's Sketchpad to draw triangles and explore the classificaiton of each using the mearsures of interior angles and the lengths of the sides.
Curated OER
Investigating Segments in a Right Triangle
High schoolers explore the concept of right triangles as they construct a right triangle using Cabri Jr. Learners find the midpoint of the hypotenuse and construct a line from the midpoint to the vertex of the right angle. They then...
Curated OER
Midsegments of a Triangle
Students analyze midsegments of triangles in this instructional activity. They use Cabri Jr. software to observe the relationships between interior angles and midsegments of triangles. Specific instructions for creating this...
Curated OER
Ratios in Right Triangles
Learners calculate the sides of right triangles in this trigonometric ratios lesson. They use Cabri Jr. software and TI-83 or TI-84 calculators to find the side lengths and their ratios to each other for various triangles. The provided...