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...

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...

Inscribed angles are central to the lesson. Young mathematicians build upon concepts learned in the previous lesson and formalize the Inscribed Angle Theorem relating inscribed and central angles. The lesson then guides learners to prove...

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...

We know theorems about circles—now what? Class members prove a theorem, with half the class taking the case where a point is inside the circle and half the class taking the case where a point is outside the circle. The lesson then...

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...

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...

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.

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...

Streets, bridges, and intersections, oh my! Parallel lines and transversals are a present in the world around us. Learners begin by discovering the relationship of the angles formed by parallel lines and a transversal. They then...

Prove the Angle Sum Theorem of a triangle using parallel line and transversal angle relationships. Pupils create a triangle from parallel lines and transversals. They find angle measures to show that the angles of a triangle must total...

Teach your learners how to investigate the relationship between a central angle and an inscribed angle which subtend the same arc of a circle. The dynamic nature of Cabri Jr. provides opportunity for conjecture and verification.

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.

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...

Circles are the foundation of many geometric concepts and extensions - a point that is thoroughly driven home in this extensive unit. Fundamental properties of circles are investigated (including sector area, angle measure, and...

Students add up the different angles using the angle addition postulate. In this geometry lesson, students differentiate between interior and exterior angles. They calculate the different angles for triangles and use proof to show their...

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...

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...

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...

Students investigate the theorems of ASA, AAS, AAA and ASA. In this geometry lesson, students discuss the theorems of triangles and how it is used to solve for missing sides or angles. They review how two angles are formed by two rays...

When going for distance, does it make a difference at what angle you launch the rocket? Teams of three launch foam rockets, varying the launch angle and determining how far they flew. After conducting the series of flights three times,...

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...

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...