The task at hand is to partition a hexagon into two, four, and eight congruent figures. Make sure to give your wizards a sheet of triangle grid paper on which to decompose the hexagons. Have them explain which rotations, reflections, or...

Very simply, geometers examine a pair of rectangles on graph paper and find a translation and rotation to demonstrate their congruence. A couple of questions follow to stimulate critical thinking about other possibilities.

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...

Your learners will make good use of the Socratic method in a collaborative task that begins with an assumed solution and ends with deeper understanding of the idea of determining two triangles congruent.

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...

Your learners collaboratively find the lines of symmetry in an equilateral triangle using rigid transformations and symmetry. Through congruence proofs they show that they understand congruence in terms of rigid motions as they...

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.

This is an interesting geometry problem. Given the figure, find the area of a triangle that is created by the intersecting lines. The solution requires one to use what he/she knows about coordinate geometry, as well as triangle...

Use the handout as guided or independent practice in drawing a reflection of a rectangle over a line. Three rectangles are provided for practice in addition to a critical thinking question.

Geometers explore symmetries of isosceles triangles by using rigid transformations of the plane. They complete four tasks, including congruence proofs, which illustrate the relationship between congruence and rigid transformations. The...

If both pairs of opposite sides of a quadrilateral are congruent, is the quadrilateral a parallelogram? This task asks learners to determine the answer and to support their answer with a proof. The resource includes a commentary for...

Now you'll never have trouble cutting a cake evenly again. Here is a set of five problems all about partitioning shapes into a given number of pieces and identifying the fractional amount of each piece. As learners progress through the...

Participants who use this resource will apply the Pythagorean Theorem to show whether or not the shaded triangle inscribed in a rectangle is a right triangle. Once all of the sides on the shaded triangle are found, it is important that...

One of the basic properties of inscribed angles gets a triangle proof treatment in a short but detailed exercise. Leading directions take the learner through identifying characteristics of a circle and how they relate to angles and...

Students, teachers, and parents alike will enjoy this challenging math site. It contains a clever brain teaser section plus creative problems related to algebra, geometry, measurement, numbers, statistics, and probability. A Spanish...

The resource investigates congruent shapes. Examples and definitions are included.

This site from The Math Forum is a great site if you are looking for activities to engage your students in learning about line symmetry. Peruse this collection of activities for one or two or four that would be right for your students....

Students learn about transformations. Topics explored are resizing, types of transformations, and congruent shapes. Examples and definitions are included.

For students who have ever played dominoes and Tetris, polyominoes will strike them as a great deal of fun. Teachers will see the educational benefits of working with similar and congruent shapes and rotating them in a plane. Exploration...

On this one page website expand your logic, symmetry and pattern recognition knowledge while working on this challenge. The solution is available to double check your solution.