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
More About Similar Triangles
Determine whether two triangles are similar. The lesson plan 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...
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
Identifying Similar Triangles
For this identifying similar triangles worksheet, 10th graders solve 5 different proofs related to similar triangles. First, they identify the similar triangles in each figure and explain why they are similar, using the information to...
Curated OER
Identify Similar Triangles With Proofs
In this similar triangle worksheet, students write a two-column proof to explain why determined triangles are similar. Given some line lengths and angle measurements, students use proofs to identify the ratio of specified angles. This...
Flipped Math
Prove Triangles Similar
Show more than one way to prove similarity. Scholars learn three different methods to show two triangles are similar, Angle-Angle, Side-Side-Side, and Side-Angle-Side. Pupils practice applying these methods to determine whether two given...
Curated OER
Triangles and Congruence
Can your class construct triangles and determine congruence? Find out with this well put together worksheet. THey construct triangles to given specifications and identify if they are congruent. There are 3 muti-step problems to solve.
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...
Curated OER
Analyzing Congruence Proofs
Looking at numerous examples of triangles, each with different properties, geometers develop their understanding of congruency. They use the notation of a counter-example to disprove certain conjectures and prove geometric theorems and...
Flipped Math
Unit 6 Review: Similar Figures
After a short review of the material from the Similar Figures Unit, pupils work through 18 problems to further practice the skills from the unit. Scholars apply those skills in the application problems at the end of the review.
University of Utah
Geometry: Angles, Triangles, and Distance
The Pythagorean Theorem is a staple of middle school geometry. Scholars first investigate angle relationships, both in triangles and in parallel lines with a transversal, before proving and applying the Pythagorean Theorem.
Curated OER
Proofs
In this proofs instructional activity, 10th graders solve and graph 8 different equations. First, they prove that each triangle is either congruent or similar. Then, students use the concept of corresponding parts of congruent triangles...
Curated OER
Congruent Triangles Homework
In this geometry instructional activity, students use proofs to solve properties of triangles. They differentiate between congruent and similar triangles. There are 15 questions.
Illustrative Mathematics
Applying the Pythagorean Theorem in a Mathematical Context
Participants who use this resource will apply the Pythagorean Theorem to show whether or not the shaded triangle inscribed in a rectangle is a right triangle. Once all of the sides on the shaded triangle are found, it is important that...
Illustrative Mathematics
Reflections and Isosceles Triangles
Geometers explore symmetries of isosceles triangles by using rigid transformations of the plane. They complete four tasks, including congruence proofs, which illustrate the relationship between congruence and rigid transformations. The...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
Curated OER
Why do Stars Rise in the East?
In this stars rise in the east worksheet, students use geometry to show how the Earth rotates from west to east and why celestial bodies appear to rise in the east and set in the west. Students draw a figure and label given points in...
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
Chapter 4.5 Geometry Practice Problems
In this geometry practice problems worksheet, students write geometric proofs to prove the validity of given circumstances. Students prove parallel lines, perpendicular lines, and similar angles. This four-page worksheet contains eight...
Curated OER
Recursion on a Calculator
In this math worksheet, students investigate repeated values on the calculator. They also read the explanation of the golden triangle and its proof.
Illustrative Mathematics
Midpoints of the Sides of a Paralellogram
This task asks learners to prove that the segment joining the midpoints of two sides of a parallelogram is both congruent and parallel to an adjacent side of the parallelogram. The activity would be good to use in a discussion about how...
Curated OER
Transformations and Congruence
In this transformations and congruence worksheet, 10th graders solve and complete 5 different types of problems. First, they calculate the length of a line giving their answer in 3 significant figures. Then, students prove that two...
EngageNY
Criterion for Perpendicularity
The Pythagorean Theorem is a geometry pupil's best friend! Learners explain the equation a1b1 + a2b2 = 0 for perpendicular segments using the Pythagorean Theorem. They are able to identify perpendicular segments using their...
Curated OER
Angles in Polygons
For this geometry worksheet, 10th graders solve problems involving quadrilaterals using the angle sum of quadrilaterals. They solve for linear pairs, opposite angle theorem and triangular angles. There are 5 questions.