How can you prove it? Guide classes through an exploration of two possible triangle congruence criteria: AAS and HL. Learners connect this criteria to those previous learned and also explore criteria that does not work. The lesson...

There isn't a more popular geometry formula than the Pythagorean Theorem! Learners understand the special side relationships in a right triangle. They use the Pythagorean Theorem to find missing sides and to solve problems. They begin...

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...

Viewers are presented with seven problems with parallel lines and angle relationships and must use the given information to find the measures of specific angles. To finish, they explain their process in finding the measures in the...

Work within a parallel universe. Scholars learn about the relationships of angles when two parallel lines are intersected by a transversal. They see how to find the measurements of all eight angles by knowing the measure of one angle....

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...

Investigate the meaning of the Pythagorean Theorem through modeling. After comparing the area of the square of each side, individuals cut triangles and squares to facilitate the comparison.

Learners watch a quick review on the Parallel and Perpendicular Lines unit. The pupils work through ten review problems ranging from identifying types of angles formed by parallel lines and transversals to writing equations of parallel...

How do dilated line segments relate? Lead the class in an activity to determine the relationship between line segments and their dilated images. In the fourth section in a unit of 16, pupils discover the dilated line...

Show it can all be proved. Scholars learn the converses of the properties of parallel lines. Using the converses, pupils determine which lines are parallel based on angle measurements and practice using a flow proof to show that two...

Intercept the class's learning on circles. Pupils learn the relationship between intercepted arcs and inscribed angles. The scholars use that information to find the relationship of angles in an inscribed quadrilateral and an angle...

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...

Your learners connect the new concepts of transformations in the coordinate plane to their previous knowledge using the solid vocabulary development in this unit. Like a foreign language, mathematics has its own set of vocabulary terms...

The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...

Determine whether two triangles are similar. The lesson presents opportunities for pupils to find the criterion needed to show that two triangles are similar. Scholars use the definition of similarity to find any missing side...

Given a diagram of connected or overlapping triangles, individuals must find congruent parts using various properties. Pictures include reflexive sides and vertical angles amongst the marked congruent parts.

Just what does it take to show two rhombuses are similar? The assessment task asks pupils to develop an argument to show that given quadrilaterals are rhombuses. Class members also use their knowledge of similar triangles to show two...

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...

What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...

Logical thinking is at the forefront of this jam-packed lesson, with young mathematicians not only investigating geometric concepts but also how they "know what they know". Through each activity and worksheet, learners wrestle with...

What do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find...

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...

Review for the test with a comprehensive list of terms and concepts for the unit on congruence and similarity. It divides divides the sections in the order of the lessons presented during the unit. 

Can they put it all together? Ninth graders apply what they know about proofs and triangle congruence to complete these proofs. These proofs go beyond the basic triangle congruence proofs and use various properties, theorems, and...