Construct yourself a winning geometry unit. A set of lessons introduces geometry scholars to constructions and proofs with compasses and straightedges. It also covers triangle congruence through transformations. This is the second of...

Allow your pupils to become the mathematicians! Individuals explore the properties of a midsegment of a triangle through construction and measurement. Once they figure out the properties, learners use them to draw conclusions.

Pupils work in pairs to investigate what it takes to prove that two triangles are similar. They work through various shortcuts to find which are enough to show a similarity relationship between the triangles. Small groups work with the...

Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...

Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...

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...

Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value...

Stretch the class' knowledge of dilations. With the aid of the rubber band stretcher tool, learners perform dilations. They dilate the triangle by a whole number scale and a fractional scale from two centers of dilation.

Using the Pythagorean Theorem to solve for missing angles, high schoolers evaluate right triangles and their properties.

Building on the previous lesson in the 29-part series, the ninth lesson asks individuals to construct a triangle given specific criteria. First, they are given three specific side lengths, followed by two sides and the included angle....

Construct an understanding of triangle congruence through a visual analysis. Young scholars find that given two sides and a non-included angle, sometimes two possible triangles are produced. Their analysis shows that if the non-included...

Middle schoolers study the triangle inequality. They will identify, compare, and analyze attributes of two and three-dimensional shapes. Then they develop vocabulary to describe the attributes. They also use manipulatives to analyze the...

Fourth and fifth graders study the Pythagorean Theorem and apply it to find the missing side of a right triangle.

Geometers employ a straight edge and compass to duplicate and bisect segments and angles, construct perpendiculars, parallel lines, figures, and circles with points of concurrency. Ample practice with 65 questions across 8 worksheets. No...

Students construct triangles. In this geometry lesson, students create equilateral triangles. They also construct triangles where the sides are different. They use the lab to create and move shapes around with the Cabri program.

There are an infinite number of points on a circle; can you find nine of them? After putting together a nine-point circle, pupils use constructions and their knowledge of triangle segments to determine the center of the circle. Learners...

Triangles, triangles, and more triangles! In this second installment of a 36-part series, your young mathematicians explore two increasingly challenging constructions, requiring them to develop a way to construct three triangles that...

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...

Drawing circles isn't the only thing compasses are good for. In this first installment of a 36-part series, high schoolers learn how to draw equilateral triangles by investigating real-world situations, such as finding the location of a...

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...

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...

Scholars explore triangles with rods of different lengths. Using rods of 2, 4, 6, 8, and 10 cm class members build as many different types of triangles as they can. They also describe properties of these triangles and determine...

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...

The Pythagorean Theorem is a staple of middle school geometry. Scholars first investigate angle relationships, both in triangles and in parallel lines with a transversal, before proving and applying the Pythagorean Theorem.