EngageNY
Definition of Congruence and Some Basic Properties
Build a definition of congruence from an understanding of rigid transformations. The lesson asks pupils to explain congruence through a series of transformations. Properties of congruence emerge as they make comparisons to these...
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....
Massachusetts Department of Education
Similarity through Transformations
Create the ultimate miniature golf course. The 93-page model curriculum unit from the Massachusetts Department of Elementary and Secondary Education contains nine lessons on understanding similarity in terms of both Euclidean geometry...
Curated OER
Similar and Congruent Shapes
In this similar-congruent activity, students determine measures of unknown angles, draw congruent shapes and determine whether shapes are congruent. A reference web site is given for additional activities.
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...
Illustrative Mathematics
Eratosthenes and the Circumference of the Earth
The class gets to practice being a mathematician in ancient Greece, performing geometric application problems in the way of Eratosthenes. After following the steps of the great mathematicians, they then compare the (surprisingly...
Curated OER
Similar Figures
In this similar figures worksheet, students identify the meaning of similar, corresponding sides, and congruent. They use proportions to find the length of a missing side. Students dilate given figures according to a scale...
Curated OER
Triangle Similarity
In this triangle similarity worksheet, 10th graders solve and complete 12 different problems that include defining similar and 3 similar statements using only sides and angles. First, they determine if each pair of triangles shown are...
Curated OER
Introduction to Fractals: Infinity, Self-Similarity and Recursion.
This lesson introduces students to the ideas involved in understanding fractals. They develop a sense of infinity, self-similarity and recursion and
Curated OER
Similar Polygons
For this geometry worksheet, students solve problems dealing with polygons. They differentiate between similar and congruent polygons. There are 18 questions with an answer key.
Curated OER
Similar Triangles
Students differentiate between similar and congruent triangles. For this geometry lesson, students identify the missing side and angle of a triangle. They identify the different ratio and proportion of the sides of a triangle.
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...
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....
Curated OER
Exploring Congruent Triangles
In this congruent triangles worksheet, learners solve 12 different equations related to writing a correspondence statement for triangles in the given diagrams. They complete each correspondence statement and write a congruence statement...
Curated OER
Symmetry and Geometric Shapes on Campus
Build on your learners' previous knowledge of geometric shapes and symmetrical figures. Then set them out to take photos of geometric shapes on campus. They assess whether the photos contain symmetry or not.
Curated OER
Similar Triangles Multiple Choice
In this triangle relationships worksheet, students identify measurements in similar and congruent triangles. Each problem features a drawing of two or more triangles. Students identify missing measurements. There are 5 multiple choice...
Curated OER
Similar Triangles - Applied Problems
High schoolers differentiate between similar and congruent triangles. In this geometry instructional activity, students identify the angles of triangles using the similarity theorem. They apply concepts of triangles to the real world.
Curated OER
Investigating Area and Perimeter of Polygons.
Student sinvestigate the area and perimeter of polygons. They differentiate between similar and congruent polygons.. They identify the ratio and proportions of the sides and angles of polygons.
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
Corresponding Parts of Similar Triangles
Here is a lesson that has learners take a look at corresponding parts of similar triangles, ratios of similarity, reductions and enlargements. They'll manipulate the scale factor (r) to observe the changes in similar triangles and then...
Charleston School District
Review Unit 2: Congruence and Similarity
Review for the test with a comprehensive list of terms and concepts for the unit on congruence and similarity. It divides divides the sections in the order of the lessons presented during the unit.
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...
Curated OER
Unit Squares and Triangles
This is an interesting geometry problem. Given the figure, find the area of a triangle that is created by the intersecting lines. The solution requires one to use what he/she knows about coordinate geometry, as well as triangle...
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...