EngageNY
Identical Triangles
Explore vocabulary and notation related to triangles and congruence. The fifth lesson in the 29-part series helps pupils build their knowledge of triangle relationships. Individuals identify corresponding parts of identical triangles and...
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,...
EngageNY
Checking for Identical Triangles II
Given a diagram of connected or overlapping triangles, individuals must find congruent parts using various properties. Pictures include reflexive sides and vertical angles amongst the marked congruent parts.
EngageNY
Using Unique Triangles to Solve Real-World and Mathematical Problems
How can congruent triangles help mark a soccer field? This is just one question your classes can answer after solving the real-world problems in the activity. Each example posed through a word problem elicits higher-order thinking and...
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...
EngageNY
Checking for Identical Triangles
Examine an assortment of triangle congruence criteria in a single instructional activity. Building on the four previous lessons of the series, the 13th installment provides a mixture of the different triangle congruence criteria for...
EngageNY
Unique Triangles—Two Sides and a Non-Included Angle
Construct an understanding of triangle congruence through a visual analysis. Young scholars find that given two sides and a non-included angle, sometimes two possible triangles are produced. Their analysis shows that if the non-included...
EngageNY
Conditions for a Unique Triangle—Two Angles and a Given Side
Using patty paper, classes determine that only one triangle is possible when given two specific angle measures and a side length. As the 10th instructional activity in the series of 29, young math scholars add these criteria to those...
EngageNY
Conditions for a Unique Triangle—Three Sides and Two Sides and the Included Angle
Building on the previous lesson in the 29-part series, the ninth lesson asks individuals to construct a triangle given specific criteria. First, they are given three specific side lengths, followed by two sides and the included angle....
EngageNY
Drawing Triangles
Create concrete examples of triangle congruence for your classes. The eighth installment of the 29-part module sets the stage for studying triangle congruence. Given a set of criteria, math scholars use constructions to build a specific...
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...
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...
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...
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...
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...
EngageNY
Similarity
Use the coordinate plane to show two figures are similar. The lesson incorporates congruence transformations and dilations to move a figure on to another figure. Pupils determine that if a similarity transformation exists...
PBS
Accessible Shapes
All the 2-D and 3-D measurement work you need is in one location. Divided into three sections, the geometry lesson plans consist of visualization of three dimensions, classifying geometric figures, and finding surface area and volume....
BW Walch
Linear & Exponential Functions
Positioned inside the framework of linear and exponential functions, this lesson is more of an investigation into the effects of changing variables and constants inside an expression. The author takes familiar formulas, those for...
EngageNY
Properties of Area
What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.
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....
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.
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...
EngageNY
How Do Dilations Map Angles?
The key to understanding is making connections. Scholars explore angle dilations using properties of parallel lines. At completion, pupils prove that angles of a dilation preserve their original measure.