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...
Mt. San Antonio Collage
Congruent Triangles Applications
Triangles are all about threes, and practicing proving postulates is a great way to get started. The first page of the worksheet provides a brief introduction of the different properties and postulates. The remaining pages contain...
Mathematics Vision Project
Congruence, Construction and Proof
Learn about constructing figures, proofs, and transformations. The seventh unit in a course of nine makes the connections between geometric constructions, congruence, and proofs. Scholars learn to construct special quadrilaterals,...
Mathematics Vision Project
Module 2: Congruence, Construction and Proof
Construct yourself a winning geometry unit. A set of lessons introduces geometry scholars to constructions and proofs with compasses and straightedges. It also covers triangle congruence through transformations. This is the second of...
Illustrative Mathematics
Why Does SSS Work?
While it may seem incredibly obvious to the geometry student that congruent sides make congruent triangles, the proving of this by definition actually takes a bit of work. This exercise steps the class through this kind of proof by...
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 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...
Illustrative Mathematics
Joining Two Midpoints of Sides of a Triangle
Without ever using the actual term, this exercise has the learner develop the key properties of the midsegment of a triangle. This task leads the class to discover a proof of similar triangles using the properties of parallel lines cut...
EngageNY
Congruence, Proof, and Constructions
This amazingly extensive unit covers a wealth of geometric ground, ranging from constructions to angle properties, triangle theorems, rigid transformations, and fundamentals of formal proofs. Each of the almost-forty lessons is broken...
Radford University
Triangular Irrigation
Try to keep the pipe short. Learners investigate where to place a water pump to use the least amount of pipe. Scholars use their knowledge of reflections and congruent triangles to find the best location for the water pump. Finally, they...
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.
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
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...
Curated OER
Reflections and Equilateral Triangles
Your learners collaboratively find the lines of symmetry in an equilateral triangle using rigid transformations and symmetry. Through congruence proofs they show that they understand congruence in terms of rigid motions as they prove...
Mathematics Vision Project
Module 6: Congruence, Construction, and Proof
Trace the links between a variety of math concepts in this far-reaching unit. Ideas that seem very different on the outset (like the distance formula and rigid transformations) come together in very natural and logical ways. This unit...
Illustrative Mathematics
Bank Shot
Young geometers become pool sharks in this analysis of the angles and lengths of a trick shot. By using angles of incidence and reflection to develop similar triangles, learners plan the exact placement of balls to make the shot....
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
Similarity
Use the coordinate plane to show two figures are similar. The lesson plan incorporates congruence transformations and dilations to move a figure on to another figure. Pupils determine that if a similarity transformation exists between...
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. It...
Curated OER
Why Does SAS Work?
Your geometry learners are guided by questions that help them use the language of reflections to explain the Side-Angle-Side congruence between two triangles in this collaborative task. Given a sample solution, declaring the triangles...
Curated OER
Why Does ASA Work?
Your geometry learners explore Angle-Side-Angle congruence in this collaborative task. The sum of the interior angles of all triangles being one hundred eighty degrees, is the key learners will discover as they explain their reasoning...
Jesuit High School
Geometry Sample Problems
I'd like to prove that this worksheet has a lot to offer. Seven problems using triangles and parallelograms practice the traditional method of a two-column proof. After the worksheet is some practice problems that show worked out...
EngageNY
The Volume Formula of a Pyramid and Cone
Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from previous...
Education Development Center
Proof with Parallelogram Vertices
Geometric figures are perfect to use for proofs. Scholars prove conjectures about whether given points lie on a triangle and about midpoints. They use a provided dialogue among fictional students to frame their responses.
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