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110 resources with the concept geometric proofs

Lesson Planet

Squaring the Triangle

For Students 8th - 12th Standards
Teach budding mathematicians how to square a triangle with an interactive that shows a graphical proof of the Pythagorean Theorem. Pupils alter the lengths of the legs using sliders. Using the inputted lengths, the applet displays the...
Lesson Planet

Diagonally Half of Me!

For Teachers 9th - 12th Standards
Cut straight to the proof. Given cutouts of different quadrilaterals, pupils draw diagonals. Learners cut up the figures along the diagonals to see whether they bisect each other. Scholars develop a geometric proof for the property they...
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Lesson Planet

How Many Ways Are There to Prove the Pythagorean Theorem?

For Students 8th - 12th Standards
There is more than one way to prove the Pythagorean Theorem. Euclid and Einstein found the same way to prove the Pythagorean Theorem. The video introduces several other ways to prove the theorem along with the history of its use.
Lesson Planet

Circle to Circle

For Students 9th - 12th Standards
What does every circle have in common? Learners explore this question as they prove all circles are similar. A series of activities leads them to this conclusion by identifying transformations.
Lesson Planet

Are All Circles Similar?

For Teachers 9th - 11th Standards
Dilated pupils, the way to prove circles are similar. Using the knowledge of dilations of polygons, class members learn how to dilate a circle to show that it is similar to any other circle. The teacher guides the class through a proof...
Lesson Planet

Proving a Rectangle Is a Parallelogram

For Students 9th - 12th Standards
Take the time to prove what seems obvious. The resource provides pupils a figure of a rectangle, which they use to develop a proof showing that the rectangle is also a parallelogram. Scholars must rely on the definition of a rectangle to...
Lesson Planet

Prove the AA Similarity Theorem

For Students 9th - 12th Standards
Transform a diagram into a proof. Given two triangles on a coordinate plane, pupils develop a proof to show they are similar. The learners use the fact that two angles of one triangle are congruent to two angles of another and their...
Lesson Planet

Prove Rhombus Diagonals Bisect Angles

For Students 9th - 12th Standards
What do congruent triangles have to do with diagonals of a rhombus? Given a rhombus, pupils develop a proof showing that a diagonal bisects opposite angles. The learners use what they know about congruent triangles to create the...
Lesson Planet

Midpoints of Sides of a Quadrilateral

For Students 9th - 12th Standards
Verify a figure by using coordinates. Pupils calculate the coordinates of the midpoints of the sides of a quadrilateral. They then use the coordinates to show the resulting figure is a parallelogram. 
Lesson Planet

Median Concurrence Proof

For Students 9th - 12th Standards
Develop a proof to show what appears to be true in a drawing actually is true. The assessment asks pupils to draw the three medians of a triangle. Learners develop a proof showing that the point of intersection in their drawing is...
Lesson Planet

IGD: Dropping a Perpendicular Line

For Students 9th - 12th Standards
Discover how circles help determine a perpendicular line. Using the applet, scholars construct the perpendicular to a line from a point. The interactive allows pupils to change the position of the line and perform each step of the...
Lesson Planet

Proof with Parallelogram Vertices

For Teachers 8th - 10th Standards
Geometric figures are perfect to use for proofs. Scholars prove conjectures about whether given points lie on a triangle and about midpoints. They use a provided dialogue among fictional students to frame their responses.
Lesson Planet

Justifying HL Congruence

For Students 9th - 12th Standards
What is so special about right triangle congruence? Pupils use what they know about transformations and right triangles to develop a proof of hypotenuse-leg congruence. The proof provides the given of two angles that measure 90 degrees...
Lesson Planet

Justifying ASA Congruence

For Students 9th - 12th Standards
Take a transformed approach to proving angle-side-angle congruence. The short assessment asks for a proof of ASA Congruence using transformations. Pupils use their knowledge of rigid motions and that congruence is preserved under them to...
Lesson Planet

Justifying SSS Congruence

For Students 9th - 12th Standards
Are congruent corresponding sides of two triangles enough to show congruence? The short assessment provides two triangles with the information that the three sets of corresponding sides are congruent. Pupils develop a proof showing that...
Lesson Planet

Justifying SAS Congruence

For Students 9th - 12th Standards
Triangle congruence is based upon rigid transformations. Given two triangles with congruent corresponding side-angle-side relationships, pupils provide a detailed description of why the two triangles must be congruent. The scholars use...
Lesson Planet

Justifying a Proof of the AA Similarity Theorem

For Students 9th - 12th Standards
Why are two triangles with congruent angles similar? Class members provide the justifications or explanations of the steps of a proof of the AA Similarity Theorem. The proof uses transformations as a basis to proving the theorem.
Lesson Planet

Isosceles Triangle Proof

For Students 9th - 12th Standards
Isosceles means two sides are congruent. Given an isosceles triangles, pupils develop a geometric proof showing that the two base angles are congruent. 
Lesson Planet

Inscribed Quadrilaterals

For Students 9th - 12th Standards
Take a supplementary look at quadrilaterals. Scholars develop a proof to show that opposite angles of a quadrilateral inscribed in a circle are supplementary. To finish, they investigate a different quadrilateral to see whether they can...
Lesson Planet

An Isosceles Trapezoid Problem

For Students 9th - 12th Standards
Prove the diagonals are shorter than the perimeter. Given an isosceles trapezoid, pupils develop a proof relating the length of the diagonals to the perimeter. Individuals sketch a graph of the trapezoid to assist with their explanations.
Lesson Planet

Equidistant Points

For Students 9th - 12th Standards
What's so special about perpendicular bisectors? Pupils investigate points on the perpendicular bisector of a line segment. They write a proof for why a point on the perpendicular bisector is equidistant from the endpoints of the line...
Lesson Planet

Diagonals of a Rectangle

For Students 9th - 12th Standards
Coordinate the vertices of a rectangle. Pupils use the location of three vertices of a rectangle along the axis to find the coordinates of the fourth vertex. Using the vertices of the rectangle, scholars prove the diagonals are congruent...
Lesson Planet

Area and Circumference 2

For Students 9th - 12th Standards
Use scale factors to find areas of circles. Pupils delve deeper into the informal argument for the formula of the area of a circle. The scholars show the relationships of areas of similar polygons also holds true for circles.
Lesson Planet

Converse of the Triangle Proportionality Theorem

For Students 9th - 12th Standards
They say the proof is in the pudding ... hopefully, in this case, the theorem isn't in there as well! Learners tackle the task of explaining the relationships between segments within a triangle. The assessment is designed to demonstrate...