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Worksheet
Curated OER

Pre-Proof Warm-Ups

For Students 10th
In this pre-proofs worksheet, 10th graders solve and complete 10 different problems that include various proofs and their definitions. They use the diagram shown and the given information to write the direct conclusion for each case....
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Unit Plan
Mathematics Vision Project

Module 3: Geometric Figures

For Teachers 9th - 12th Standards
It's just not enough to know that something is true. Part of a MVP Geometry unit teaches young mathematicians how to write flow proofs and two-column proofs for conjectures involving lines, angles, and triangles.
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Lesson Plan
1
1
Illustrative Mathematics

Similar Triangles

For Teachers 9th - 11th Standards
Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...
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Interactive
CK-12 Foundation

Parallelogram Proofs: Quadrilaterals that are Parallelograms

For Students 6th - 12th
What conditions must be met for a quadrilateral to be a parallelogram? A slider interactive allows individuals to move the vertices of a quadrilateral. They answer questions that prove whether a given quadrilateral is a parallelogram.
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Worksheet
Curated OER

Using Proof in Algebra

For Students 10th
In this using proofs in algebra activity, 10th graders solve 2 proofs by applying the many rules from algebra for the Properties of Equality for real numbers. They name the property that justifies each statement as seen in the...
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Worksheet
Curated OER

Proofs: Solving Equations

For Students 9th - 12th
In this proofs worksheet, high schoolers solve 4 short answer problems. Students identify the correct reason for each step in solving each multi-step equation.
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Lesson Plan
Curated OER

Getting It Right! An Investigation of the Pythagorean Theorem

For Teachers 6th - 8th
Learners construct a variety of right triangles using a right-angled set square, cutting corners from pieces of paper or cardboard, and using dynamic geometry software. They measure the sides of these various right triangles and record...
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Instructional Video11:57
2
2
Flipped Math

Side Splitter Theorem

For Students 9th - 12th Standards
Apply perspective to similarity. Individuals learn about the Side Splitter Theorem by looking at perspective drawings. Pupils use the theorem and its corollary to find missing lengths in figures. Next, they practice using the theorem and...
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Lesson Plan
EngageNY

Congruence Criteria for Triangles—ASA and SSS

For Students 9th - 10th Standards
How do you know if a pair of triangles are congruent? Use the lesson to help class members become comfortable identifying the congruence criteria. They begin with an exploration of ASA and SSS criteria through transformations and...
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Lesson Plan
EngageNY

Special Lines in Triangles (part 2)

For Teachers 9th - 10th Standards
Medians, midsegments, altitudes, oh my! Pupils study the properties of the median of a triangle, initially examining a proof utilizing midsegments to determine the length ratio of a median. They then use the information to find missing...
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Lesson Plan
EngageNY

Congruence Criteria for Triangles—SAS

For Students 9th - 10th Standards
Looking for a different approach to triangle congruence criteria? Employ transformations to determine congruent triangles. Learners list the transformations required to map one triangle to the next. They learn to identify congruence if...
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Lesson Plan
EngageNY

Looking More Carefully at Parallel Lines

For Students 9th - 10th Standards
Can you prove it? Making assumptions in geometry is commonplace. This resource requires mathematicians to prove the parallel line postulate through constructions. Learners construct parallel lines with a 180-degree rotation and then...
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Lesson Plan
EngageNY

Review of the Assumptions (part 2)

For Students 9th - 10th Standards
Is the amount of information getting overwhelming for your geometry classes? Use this strategy as a way to organize information. The resource provides a handout of information studied in relation to triangle congruence. It includes a...
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Lesson Plan
Curated OER

Geometry, Measurement & Reasoning

For Teachers 9th - 11th
Students construct two-column proofs. In this geometry instructional activity, students use deductive reasoning and geometric properties to justify given geometric statements. Students compare and contrast proofs.
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Lesson Plan
Curated OER

Paragraph Proofs

For Teachers 9th - 12th
Students explore the concept of paragraph proofs. For this paragraph proofs lesson, students make flow charts of the process of getting ready for school. Students convert the flow chart to a paragraph proof. Students use geometric...
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Worksheet
Curated OER

Indirect Euclidean Proofs

For Students 10th
In this Euclidean proofs worksheet, 10th graders solve 10 different problems that include completing indirect Euclidean proofs. First, they write a statement for each of the reasons listed on the sheet of proofs. Then, students solve the...
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Worksheet
Curated OER

Indirect Euclidean Proofs

For Students 7th - 8th
In this indirect Euclidean proof worksheet, students write statements supporting the reasons for a given proof. This one-page worksheet contains ten problems.
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Worksheet
Curated OER

Quiz: Beginning Congruent Triangle Proofs

For Students 10th - 11th
In this congruent triangle proof worksheet, students write theorems to prove the congruence of given triangles. This one-page worksheet contains three given polygons to prove congruence.
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Lesson Plan
Curated OER

The Truth About Triangles And Proofs

For Teachers 9th - 12th
Students engage in a lesson that is about the classification of triangles and the mathematical proofs involved in working with them. They work on a variety of problems that are created by the teacher with the focus upon the importance of...
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Lesson Plan
EngageNY

Solve for Unknown Angles—Angles and Lines at a Point

For Teachers 9th - 10th Standards
How do you solve for an unknown angle? In this sixth installment of a 36-part series, young mathematicians use concepts learned in middle school geometry to set up and solve linear equations to find angle measures.
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Lesson Plan
EngageNY

Proving the Area of a Disk

For Teachers 9th - 10th Standards
Using a similar process from the first lesson in the series of finding area approximations, a measurement resource develops the proof of the area of a circle. The problem set contains a derivation of the proof of the circumference formula. 
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Lesson Plan
EngageNY

Properties of Parallelograms

For Teachers 9th - 10th Standards
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...
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Lesson Plan
EngageNY

Ptolemy's Theorem

For Teachers 9th - 12th Standards
Everyone's heard of Pythagoras, but who's Ptolemy? Learners test Ptolemy's Theorem using a specific cyclic quadrilateral and a ruler in the 22nd installment of a 23-part module. They then work through a proof of the theorem.
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Instructional Video15:58
2
2
Flipped Math

Reasoning and Proof

For Students 9th - 12th
Make sure the conditions are right. Pupils watch a video introducing conditional statements and their related statements. Learners find out how to identify the hypothesis and conclusion as well as write the converse, inverse, and...

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