This amazingly extensive unit covers a wealth of geometric ground, ranging from constructions to angle properties, triangle theorems, rigid transformations, and fundamentals of formal proofs.  Each of the almost-forty lessons...

Middle and high schoolers construct a triangle using Cabri Jr. They construct squares on each of the legs and hypotenuse of the triangle. Pupils show that the area of the squares on the leg equal the area of the square on the hypotenuse.

Prove the Pythagorean Theorem using multiple informal proofs. Scholars first develop an understanding of the origins of the Pythagorean Theorem through proofs. They round out the lesson by using the theorem to find missing side lengths...

Provide your emerging mathematicians with the tools to learn as they incorporate auxiliary lines to solve unknown angle proofs in this continuing segment. They decipher information from a diagram to uncover the missing pieces and...

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.

A diameter is the longest chord possible, but that's not the only relationship between chords and diameters! Young geometry pupils construct perpendicular bisectors of chords to develop a conjecture about the relationships between chords...

Build confidence in proofs by proving a known property. Pupils explore two approaches to proving base angles of isosceles triangles are congruent: transformations and SAS. They then apply their understanding of the proof to more complex...

Students define inductive and deductive reasoning and write two column proofs. In this geometry lesson, students analyze arguments and draw conclusion. They define steps necessary to arrive at the correct answer when completing proofs.

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...

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...

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...

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...

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.

Learners complete two column proofs. In this geometry lesson,students derive the reasons their answers are correct using logic. They write the proof step by step using two columns.

Lead the class in a Greek history lesson plan 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...

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....

Students investigate proofs used to solve geometric problems. In this geometry lesson, students read about the history behind early geometry and learn how to write proofs correctly using two columns. The define terminology valuable to...

Young scholars discuss the importance of examining crystals and experiment growing them. In groups, they complete a project in which they use groups in geometry just like crystallographers. They practice solving the groups and proofs...

The Pythagorean Theorem is a geometry pupil's best friend! Learners explain the equation a1b1 + a2b2 = 0 for perpendicular segments using the Pythagorean Theorem. They are able to identify perpendicular segments using their...

Assist your class with each angle of geometry as they use exterior angles to form linear pairs with adjacent interior angles. They cover multiple vocabulary terms and work practice problems, complete with justifications, before...

Isn't paper pushing supposed to be boring? Learners attempt a paper-pushing puzzle to develop ideas about angles inscribed on a diameter of a circle. Learners then formalize Thales' theorem and use geometric properties to develop a proof...

No height? No problem! Learners use their knowledge and a little help from GeoGebra to develop the Law of Sines formula. The Law of Sines helps to determine the height of triangles to calculate the area.

Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once...

Students explore the concept of tessellations. In this tessellations lesson, students use an applet to construct tessellations. Students use regular polygons to construct tessellations. Students find patterns and symmetry in their...