Curated OER
Coordinate Proofs
High schoolers explore the concept of coordinate proofs. In this coordinate proofs lesson plan, students write coordinate proofs using properties of distance, slope, and midpoint. High schoolers discuss why it is sometimes beneficial to...
EngageNY
Tangent Segments
What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...
Inside Mathematics
Circles in Triangles
Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...
EngageNY
Characteristics of Parallel Lines
Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...
EngageNY
Properties of Parallelograms
Everyone knows that opposite sides of a parallelogram are congruent, but can you prove it? Challenge pupils to use triangle congruence to prove properties of quadrilaterals. Learners complete formal two-column proofs before moving on to...
EngageNY
Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
EngageNY
How Do Dilations Map Segments?
Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions.
Curated OER
Tangram Perimeters
Middle schoolers work together to make figures out of tangram squares. In groups, they calculate the measurements they need and apply the Pythagorean Theorem. They complete a worksheet solving equations using the theorem and review their...
Curated OER
Flying with Pythagoras
A lengthy narrative about Pythagoras and his students precedes an activity in which your young mathematicians practice using the Pythagorean theorem to solve three problems about flight and distance. Answers are provided.
Curated OER
More Congruent Triangles
For this congruent triangles worksheet, 10th graders solve 5 various types of geometry problems related to triangles. First, they draw and label triangles, indicating the additional pairs of corresponding parts that would have to be...
Curated OER
Proving Triangles Congruent
In this proving triangles congruent learning exercise, 10th graders solve 5 different problems that include proofs and proving congruence in triangles. First, they determine which postulate can be used to prove the triangles congruent...
Curated OER
Angles in Polygons
In this geometry worksheet, 10th graders solve problems involving quadrilaterals using the angle sum of quadrilaterals. They solve for linear pairs, opposite angle theorem and triangular angles. There are 5 questions.
Curated OER
Why Doesn't SSA Work?
Students investigate the relationship between angles and their sides. For this geometry lesson, students prove why SSA does not work as a true angle side relationship theorem.
Curated OER
Four Color Theorem
Students identify and interpret how the Free Response questions are graded on an AP Exam. They also discuss coloring the included map, placing several examples on the board to determine the number of colors necessary to color each....
Inside Mathematics
Rhombuses
Just what does it take to show two rhombuses are similar? The assessment task asks pupils to develop an argument to show that given quadrilaterals are rhombuses. Class members also use their knowledge of similar triangles to show two...
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...
Curated OER
MOTION IN A CIRCLE
Students explore uniform circular motion, and the relation of its frequency of N revolutions/sec with the peripheral velocity v and with the rotation period T, and the "centripetal acceleration" of an object.
Curated OER
Pape's Theorems
In this math worksheet, students find the length of the side of a regular hexagon whose area is numerically equal to its perimeter.
Curated OER
The Chain Rule and Applications
In this chain rule worksheet, students use the chain rule to differentiate compositions, and determine the value of the limits. They give reasons justifying each step of the chain theorem. This six-page worksheet contains theorems,...
Curated OER
Determining Angle Measure with Parallel Lines
Students observe and solve examples of corresponding angle postulates, alternate interior angle theorems, and exterior and consecutive angles. They complete the Determining Angle Measure With Parallel Lines worksheet.
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
The Shortest Distance
Students, working on their GED, examine the steps used to resolve the unknown sides of a right triangle. They express the square root function as an exponential function and derive the distance formula using principles of geometry.
Curated OER
Drawing Straws
Fourth graders examine the Triangle Inequality Theorem by investigating possible lengths of the sides of a triangle.
Curated OER
Using Properties Multiple Choice
In this geometry worksheet, students identify the different properties to represent a given statement. They use proof to show how they arrived at their answer. There are 5 questions with an answer key.