EngageNY
More About Similar Triangles
Determine whether two triangles are similar. The lesson presents opportunities for pupils to find the criterion needed to show that two triangles are similar. Scholars use the definition of similarity to find any missing side...
Mathematics Assessment Project
Identifying Similar Triangles
Math whizzes work with angle sums and exterior angles to figure out the measure of other angles. This particular publication provides comprehensive support in the form of an anticipatory activity, questions designed to prompt discussion,...
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...
West Contra Costa Unified School District
Investigating Similar Triangles
Let your use of the resource be in proportion to its usefulness. Pupils investigate similar triangles by measuring side lengths and considering given angle measures. The results of the investigation help develop generalizations about...
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...
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...
EngageNY
Basic Properties of Similarity
Does the symmetry and transitive property apply to similarity? The 10th segment in a series of 16 presents the class with a group of explorations. The explorations have pairs show that similarity is both symmetrical and transitive....
Curated OER
Triangle's Interior Angles
Given a pair of parallel lines and a triangle in between, geometers prove that the sum of the interior angles is 180 degrees. This quick quest can be used as a pop quiz or exit ticket for your geometry class.
EngageNY
Proof of the Pythagorean Theorem
What does similarity have to do with the Pythagorean Theorem? The activity steps through the proof of the Pythagorean Theorem by using similar triangles. Next, the teacher leads a discussion of the proof and follows it by an animated...
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...
Mathematics Assessment Project
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...
EngageNY
Similarity
Learn similarity through a transformations lens! Individuals examine the effects of transformations and analyze the properties of similarity, and conclude that any image that can be created through transformations is similar. The...
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...
Curated OER
Exploring Polygons and The Greedy Triangle
Excellent lesson plan! 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),...
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...
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...
EngageNY
Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
Curated OER
Similar Figures
Your class will use a TI calculator to drag vertices of rectangles and triangles to observe what happens to ratios of pairs of sides within each figure. They will apply the definition of similarity to identify similar shapes. The...
Curated OER
When Does SSA Work to Determine Triangle Congruence?
Your learners will make good use of the Socratic method in a collaborative task that begins with an assumed solution and ends with deeper understanding of the idea of determining two triangles congruent.
Curated OER
Angles and Similarity
High schoolers identify triangles as similar or congruent. In this geometry lesson, students drag triangles around on the navigator to see the effect of different angles on the shape of the triangle. They discuss angle similarity and...
Curated OER
Proofs of the Pythagorean Theorem
Working individually and collaboratively, geometers gain a clear understanding of the Pythagorean theorem. They create, explain, and compare proofs of the theorem. Proofs involve areas of trapezoids, squares, and triangles, congruent...
Curated OER
The Minimal Distance Point from the Vertices of a Triangle
Students calculate the distance from the vertex of a triangle to the center. For this geometry lesson, students find the shortest distance between a point and the vertex of a triangle. They relate this concept of distance to the real world.
EngageNY
Congruence Criteria for Triangles—SAS
Looking for a different approach to triangle congruence criteria? Employ transformations to determine congruent triangles. Learners list the transformations required to map one triangle to the next. They learn to identify congruence...
Illustrative Mathematics
Find the Change
This exercise is an opportunity for algebra learners to understand the connection between the slope of a line and points found on the line. Use similar triangles to explain why slope m is the same between any two points. Discuss with the...