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Illustrative Mathematics
Sum of Angles in a Polygon
How can learners use algebra to solve a geometry problem? Help learners create an equation that shows the relationship between the number of sides of a polygon and the sum of the interior angles. Students are asked to divide the...
Curated OER
Tile Patterns II: Hexagons
After learning that the sum of interior angles for triangles is 108 degrees, take it further to show that the sum of angles in any polygon is the same! Using hexagons, pupils practice finding the measure of the six congruent angles. Make...
Curated OER
Triangle's Interior Angles
Given a pair of parallel lines and a triangle in between, geometers prove that the sum of the interior angles is 180 degrees. This quick quest can be used as a pop quiz or exit ticket for your geometry class.
EngageNY
Angle Sum of a Triangle
Prove the Angle Sum Theorem of a triangle using parallel line and transversal angle relationships. Pupils create a triangle from parallel lines and transversals. They find angle measures to show that the angles of a triangle must total...
Mathematics Assessment Project
Identifying Similar Triangles
Math whizzes work with angle sums and exterior angles to figure out the measure of other angles. This particular publication provides comprehensive support in the form of an anticipatory activity, questions designed to prompt discussion,...
Virginia Department of Education
Angles in Polygons
Polygons — it's all about the angles. Groups work with dynamic geometry software to find the sum of the measures of the angles of various polygons. After finding the information for several polygons, the groups generate a formula that...
Curated OER
Geometry In Space
How can we identify shapes in the Universe? High schoolers will compare and contrast elliptic and hyperbolic geometry. They will also explore one possible way to measure the curvature of the Universe, namely, by measuring the sum of the...
EngageNY
Solve for Unknown Angles—Angles in a Triangle
Assist your class with each angle of geometry as they use exterior angles to form linear pairs with adjacent interior angles. They cover multiple vocabulary terms and work practice problems, complete with justifications, before...
Curated OER
Measuring Angles in a Quadrilateral
High schoolers explore quadrilaterals in this geometry lesson. They will draw a quadrilateral, measure the angles, and find the sum of the measures of the interior angles using Cabri Jr. The interactive capabilities of Cabri Jr. allow...
EngageNY
Unknown Angle Proofs—Proofs of Known Facts
Lead the class in a Greek history lesson with a geometric twist. Pupils relate a short video about geometric properties to modern-day methods of solving for unknown angles. They discuss parallel line theorems and complete...
Hotchalk
Triangle Sum Theorem
Your visual geometry learners will appreciate triangle drawings as they model the triangle sum theorem and algebraically solve to find the missing interior angle in a triangle. Practice problems increase in complexity and vary in their...
Curated OER
Angle Relationships
Students investigate geometric relationship using conjecture about linear pairs and vertical angles. In this geometry activity, students apply their theorems and previous geometry knowledge to solve for and find angles of...
Virginia Department of Education
How Many Triangles?
Something for young mathematicians to remember: the sum of any two sides must be greater than the third. Class members investigates the Triangle Inequality Theorem to find the relationship between the sides of a triangle. At the...
Curated OER
Measuring Angles in a Triangle
High schoolers investigate the sum of the measures of the angles of a triangle. They draw a triangle and measure the interior angles. Using Cabri Jr., learners find the sum of the measures of the interior angles. The lesson provides an...
Curated OER
Angles of a Triangle
Learners explore the measures of the angles of a triangle in this geometry lesson plan. They use Cabri Jr. to investigate the sum of the measures of the interior angles of a triangle, and examine the relationships between the interior...
Curated OER
Sum of Exterior Angles of Polygons
Have fun calculating angles for different polygons. The class differentiate the relationship between the interior and exterior angles of polygons. They discuss linear pair as it related the polygons and their angles. This is done as they...
Curated OER
Patterns in the Sums of Polygon Angles
Sixth graders discover the patterns of sums of polygon angles. In this math lesson, 6th graders study the properties of geometric shapes to solve problems as they participate in hands-on activities.
Curated OER
Interior/Exterior Polygon Angles and Tessellations
Students discover the sum of the interior and exterior angles of several polygons. In this Geometers sketchpad lesson, students work in groups to find the stated measurements of triangles, quadrilaterals, pentagons and hexagons. Students...
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
Geometry Journal: Isosceles Triangles
For this isosceles triangles worksheet, students justify and determine the symmetry of an isosceles triangle. They explore the bisector of rectangles. This three-page worksheet contains two problems. Answers are listed on page three.
Curated OER
Tile Patterns I: Octagons and Squares
This can be used as a critical thinking exercise in congruence or as a teaching tool when first introducing the concept. Four octagons are arranged in such a way that a square is formed in the middle. With this information, geometry...
Improving Measurement and Geometry in Elementary Schools
The Sum of the Interior Angles of a Polygon
Junior geometers discover that polygons can be decomposed into triangles and that the number of triangles can be determined by a rule. Note that the Geometer’s Sketchpad® software is required to carry out all components of this...
Curated OER
Betweenness and the Sum of Parts
High schoolers differentiate lines and angles using betweenness in this geometry lesson. They differentiate angles and lines using Cabri Jr. and analyze the data and make conjecture.
Curated OER
The Sum of All Angles
Students add up the different angles using the angle addition postulate. In this geometry lesson, students differentiate between interior and exterior angles. They calculate the different angles for triangles and use proof to show their...