West Contra Costa Unified School District
The Parallelogram Law
Use your pupils' sense of curiosity to explore the Parallelogram Law. Here is an activity that outlines a complete lesson plan from beginning to end, allowing pupils to follow a conjecture through to the proof stage.
EngageNY
Unknown Angle Proofs—Writing Proofs
What do Sherlock Holmes and geometry have in common? Why, it is a matter of deductive reasoning as the class learns how to justify each step of a problem. Pupils then present a known fact to ensure that their decision is correct.
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...
EngageNY
Proofs of Laws of Exponents
Apply pupil understanding of exponent properties to prove the relationships. In the sixth instructional activity of the series, individuals are expected to prove relationships using mathematical statements and reasoning.
EngageNY
Analytic Proofs of Theorems Previously Proved by Synthetic Means
Prove theorems through an analysis. Learners find the midpoint of each side of a triangle, draw the medians, and find the centroid. They then examine the location of the centroid on each median discovering there is a 1:2 relationship....
Chapman University
Proof of L’Hospital’s Rule
Understanding how calculus formulas were derived connects learners to the idea that the study of mathematics is continuous and cumulative. Learners will also develop a deeper appreciation for the derivative's application in...
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
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...
Old Dominion University
Introduction to Calculus
This heady calculus text covers the subjects of differential and integral calculus with rigorous detail, culminating in a chapter of physics and engineering applications. A particular emphasis on classic proof meshes with modern graphs,...
West Contra Costa Unified School District
Derivation of the Quadratic Formula
What connection does the quadratic formula have with a quadratic equation? Using a matching activity, pupils construct the algebraic derivation of the quadratic formula in this Algebra II lesson task. The task provides two variations of...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
Texas Education Agency (TEA)
Proofreading
Where's the proof? Using the resource, scholars learn proofreading marks and complete a series of worksheets to practice using them correctly. Then, they make intentional errors to a writing passage before switching with a partner to...
Curated OER
Verifying Segment Relationships
In this verifying segment relationships worksheet, 10th graders solve 3 different proofs by verifying the segment relationship in each. They complete each proof given a specific statements supporting the statement with reasons. Then,...
Curated OER
Verifying Segment Relationships
In this verifying segment relationships activity, 10th graders solve two proofs by following the same format used in algebra. They complete each of two proofs by naming the property that justifies each statement given. Students also...
Curated OER
Proving Triangles Congruent
In this proving triangles congruent instructional activity, 10th graders solve 4 different proofs for congruent triangles. First, they mark all congruent parts on each figure, then complete the prove statement and identify the postulate...
Curated OER
Identifying Similar Triangles
For this identifying similar triangles worksheet, 10th graders solve 5 different proofs related to similar triangles. First, they identify the similar triangles in each figure and explain why they are similar, using the information to...
Curated OER
Parallelograms
In this parallelograms worksheet, 10th graders solve 8 different types of problems related to measuring various parallelograms. First, they use the figure, a parallelogram, illustrated at the top to solve each problem. Then, students...
Curated OER
Verifying Angle Relationships
In this angle relationships learning exercise, 10th graders solve 8 various problems related to verifying angle relationships. First, they complete each statement if the measure of specific angles are equal to 43 and 56. Then, students...
Curated OER
Using Properties Homework
In this geometry worksheet, 10th graders determine the property of the real number system that justifies each given statement and complete a two column proof in which they justifying the steps for solving an equation. The one page...
Curated OER
Tests for Parallelograms
In this tests for parallelograms worksheet, 10th graders solve 7 various forms of questions that relate to testing for parallelograms in the figures shown. First, they find the values of x and y that insure each quadrilateral is a...
Curated OER
Proving Quadrilateral Properties
Working backwards can sometimes help you see a path to solving a problem. In this chapter, properites of quadrilaterials are proven by looking at flowcharts and working the probem backwards. Worked through examples are given, along with...
Curated OER
The Pythagorean Theorem Lesson 2
Learners discuss and review examples of the Pythagorean Theorem using a GSP, Geometer's Sketchpad, activity.
Curated OER
Proving Triangles Congruent
In this proving triangles congruent activity, 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 and mark...
Curated OER
Right Triangles
In this right triangles worksheet, 10th graders solve 5 problems that relate to different right triangles. First, they find the values of x and y so that each triangle is congruent to the other. Then, students write a two-column proof...
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