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...
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
Similarity and the Angle Bisector Theorem
Identifying and verifying reproducible patterns in mathematics is an essential skill. Mathematicians identify the relationship of sides when an angle is bisected in a triangle. Once the pupils determine the relationship, they prove it to...
EngageNY
Prove the Pythagorean Theorem Using Similarity
Amaze your classes with the ability to find side lengths of triangles immediately — they'll all want to know your trick! Learners use the Pythagorean Theorem and special right triangle relationships to find missing side lengths.
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...
Mathalicious
Been Caught Stealing
You're safe, when calculating the odds of stealing second base! Learners compare the rate of a runner to the distance the ball travels, in a lesson that explores right triangles and measurement. Full of discussion questions and fun...
Curated OER
You Can't Go Wrong with a Right Triangle 2
Upper graders use the properties of right angle trignonmetry to measure objects such as the school flagpole. They solve real world problems using these properties.
Inside Mathematics
Rhombuses
Just what does it take to show two rhombuses are similar? The assessment task asks pupils to develop an argument to show that given quadrilaterals are rhombuses. Class members also use their knowledge of similar triangles to show two...
Inside Mathematics
Hopewell Geometry
The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...
EngageNY
Comparing the Ratio Method with the Parallel Method
Can you prove it? Lead your class through the development of the Side Splitter Theorem through proofs. Individuals connect the ratio and parallel method of dilation through an exploration of two proofs. After completing the proofs,...
Mathematics Vision Project
Similarity and Right Triangle Trigonometry
Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...
EngageNY
Families of Parallel Lines and the Circumference of the Earth
How do you fit a tape measure around the Earth? No need if you know a little geometry! Pupils begin by extending their understanding of the Side Splitter Theorem to a transversal cut by parallel lines. Once they identify the proportional...
Curated OER
Parallel Lines and Proportional Parts
In this parallel lines and proportional parts worksheet, 10th graders solve 6 problems that include applying the theorems involved in proportional parts of triangles. First, they identify and describe each theorem. Then, students find...
Curated OER
Similar Triangles - Applied Problems
Students differentiate between similar and congruent triangles. In this geometry lesson plan, students identify the angles of triangles using the similarity theorem. They apply concepts of triangles to the real world.
Curated OER
Mean Twisters - Mean Proportional
In this mean proportional activity, learners work in pairs to solve right triangle problems. They use ratios and proportions of similar triangles to determine a missing length. This two-page activity contains 16 problems.
Curated OER
Pythagorean Theorem
Students solve problems using the Pythagorean Theorem. In this geometry lesson, students identify different parts of a right triangle. They use the Pythagorean Theorem to calculate missing angles and sides.
Curated OER
Similar Triangles
Ninth graders find the height of every day objects using techniques learned through postulates that allow triangles in a problem to be similar. They calculate the length of a missing side and solve proportions.
Curated OER
The Right Stuff
Young scholarsare introduced to the Pythagorean Theorem by exploring right triangles and the squares built on each side. They apply the Pythagorean Theorem to real-world problems. Students u se informal and nonformal arguments of proof...
Curated OER
Proportions
In this proportion worksheet, students compare two proportionate shapes and find the length of the "x" side. There are four pairs of shapes. Shapes include triangle, rectangle, parallelogram and a trapezoid.
Curated OER
Side Splitter Triangles
Students investigate the side splitter theorem. For this geometry lesson, students estimate and solve problems dealing with ratios and proportions. They identify angles created by lines that are parallel.
Curated OER
Proportional Parts Homework
In this geometry activity, students differentiate between similarity and proportion. They use scale factor as they solve for the different proportions. There are 15 questions.
Curated OER
Similarity and Congruence
Students determine that two figures are similar or congruent by
investigating figures that are similar and figures that are congruent. They prove that two figures are similar or congruent by using definitions,
postulates, and theorems.
Curated OER
Using Proportions Self Check Quiz
In this geometry activity, students identify the different ratios of triangles using the theorems. They use SSS, SAS, ASA and AAS to differentiate between triangles. There are 7 questions with an answer key.
Curated OER
Similarity: Instructional
In this similarity learning exercise, students solve and complete 7 different problems that include determining various dimensions of mirrors shown. First, they find the length of the diagonal of the large mirror in the diagram. Then,...