Balanced Assessment
Refiguring Pythagoras
Why was Pythagoras so obsessed with squares? The assessment task posits the question of whether the geometric interpretation of the Pythagorean Theorem holds for figures other than squares. Scholars first consider the case of semicircles...
EngageNY
The Converse of the Pythagorean Theorem
Is it a right triangle or not? Introduce scholars to the converse of the Pythagorean Theorem with a lesson that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether triangles with given...
Virginia Department of Education
Pythagorean Theorem
Investigate the meaning of the Pythagorean Theorem through modeling. After comparing the area of the square of each side, individuals cut triangles and squares to facilitate the comparison.
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
Unknown Angles
How do you solve an equation like trigonometry? Learners apply their understanding of trigonometric ratios to find unknown angles in right triangles. They learn the meaning of arcsine, arccosine, and arctangent. Problems include basic...
Mathematics Assessment Project
Deducting Relationships: Floodlight Shadows
Try to figure out what happens with shadows as a person moves between two light sources. A formative assessment lesson has individuals work on an assessment task based on similar triangles, then groups them based on their assessment...
EngageNY
From Circle-ometry to Trigonometry
Can you use triangles to create a circle? Learners develop the unit circle using right triangle trigonometry. They then use the unit circle to evaluate common sine and cosine values.
Arizona Department of Education
Area and Perimeter of Regular and Irregular Polygons
Extend young mathematicians' understanding of area with a geometry lesson on trapezoids. Building on their prior knowledge of rectangles and triangles, students learn how to calculate the area of trapezoids and other irregular...
Illustrative Mathematics
Two Wheels and a Belt
Geometry gets an engineering treatment in an exercise involving a belt wrapped around two wheels of different dimensions. Along with the wheels, this belt problem connects concepts of right triangles, tangent lines, arc length, and...
EngageNY
Modeling Using Similarity
How do you find the lengths of items that cannot be directly measured? The 13th installment in a series of 16 has pupils use the similarity content learned in an earlier resource to solve real-world problems. Class members determine...
Mathwire
Shamrock Paths
What could St. Patrick's Day and Pascal's triangle possibly have in common? Trace the pattern in a holiday-themed activity that prompts learners to find the word shamrock as many times as they can.
DK Publishing
Draw the Shape ~ Counting Triangles
Starting simply, scholars begin by tracing two triangles before drawing one or two on their own. Next, they examine three pictures to determine how many triangles they see in each. Learners record their answers, practicing writing...
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....
CK-12 Foundation
Logarithms: Logarithm Triangle
Study logarithmic properties using a triangle. A clever manipulative shows how a triangle can represent the three parts of a logarithmic or exponential equation. Pupils review the concept and then answer guiding questions to further...
Flipped Math
Reference Triangles
It is all about where the side is located. Pupils use their knowledge of angles in standard position to find reference angles. They use the Pythagorean Theorem to find lengths along a terminal side of an angle to determine the exact...
Center for History Education
The Triangle Shirtwaist Factory Fire: Is Anyone to be Punished for This?
The stories of bodies falling to the pavement and girls dying in their seats echo to the present day. The New York City Triangle Shirtwaist Factory fire—which killed 147 people, mostly young women and girls—galvanized the labor movement...
Curated OER
Classifying Triangles Based On Properties of Angles
The interactive instructional activity featured here calls for the use of a Smartboard for sorting and classifying shapes. Then, pupils discuss the rules they followed for sorting their shapes, particularly focusing on the properties of...
Curated OER
Triangles
In this triangles learning exercise, students identify 3 triangles by the length of their sides and 3 triangles according to their internal angles.
Curated OER
Counting Triangles
Sixth graders examine triangles in a figure. In this geometry instructional activity, 6th graders establish a method for counting triangles within a given figure. Students discover that the total number of triangles is the sum of all...
Curated OER
Testing For Congruent Triangles
Students define and discuss congruency and the corresponding parts between congruent triangles. They create a pair of congruent triangles, test for congruency, and complete a worksheet.
Curated OER
Right Triangles
In this right triangles worksheet, 10th graders solve 6 various problems and figures related to right triangles. First they identify and describe the 3 theorems and 1 postulate stated that prove 2 right triangles congruent if one of them...
Curated OER
Quiz: Triangle Inequality Theorem
In this triangle inequality theorem activity, students determine the lengths of the sides of triangles and identify the measure of angles. This one-page activity contains ten triangle theorem problems.
Curated OER
Triangle Attributes and Measures
Seventh graders explore the concept of triangles. In this triangles lesson, 7th graders sort triangles according to various attributes such as acute, obtuse, isosceles, or equilateral. Students find the area and perimeter of triangles.
Curated OER
Types of Triangles
Learners classify triangles by the length of their sides. In this geometry lesson, students use a white board to demonstrate the angles of various triangles. Learners construct an equilateral, isosceles, and a scalene triangle.
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