Determine whether two triangles are similar. The instructional activity 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...

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...

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...

Looking for a strategy to organize the information related to transformations? The materials ask pupils to identify a sequence of rigid transformations, identify corresponding angles and sides, and write a congruence statement. They...

Determine whether it is right or not. Using the Pythagorean Theorem, the video shows how to determine whether a triangle is a right triangle. Pupils practice the skill in a few of the problems in the associated worksheets on the...

Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...

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...

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...

Corresponding parts, congruent parts, congruent corresponding parts—what does it all mean? The resource challenges pupils to identify corresponding parts for pairs of figures. It uses examples of figures that undergo rigid...

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...

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.

Triangles are all about threes, and practicing proving postulates is a great way to get started. The first page of the worksheet provides a brief introduction of the different properties and postulates. The remaining pages contain...

Playing with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...

Looking to challenge your students that have mastered basic triangle congruence proofs? A collection of proofs employ previously learned definitions, theorems, and properties. Pupils draw on their past experiences with proofs to...

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...

Use some similar problems to find side lengths. Pupils learn the definition of similar figures and how it relates to corresponding angles and sides. Using the definition, individuals calculate the lengths of missing sides and practice...

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...

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...

How do you find the lengths of items that cannot be directly measured? The 13th installment in a series of 16 has pupils use the similarity content learned in an earlier resource to solve real-world problems. Class members determine...

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...

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.

Geometry is full of shapes, figures, and corresponding things here and there. The guide shares all of the key pieces of geometric information in a nicely color-coded and labeled sheet. 

Tie the unit together and see concepts click in your young mathematicians' minds. Scholars apply the properties of similar triangles to find heights of objects. They concentrate on the proportions built with known measures and solve to...

Investigate how similar and congruent figures compare. Learners understand congruent figures have congruent sides and angles, but similar figures only have congruent angles — their sides are proportional. After learning the...