Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...

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...

Challenge the class to prove that the dilation properties always hold. The lesson develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member performing the...

Explore angle relationships associated with transversals. Pupils construct parallel lines with a transversal and find the measures of the angles formed. They figure out how the different angles are related before constructing...

Tenth graders explore parallel and perpendicular lines.  In this geometry lesson, 10th graders investigate the relationships associated with parallel lines and transversals, perpendicular lines, and the angles formed by these...

Without ever using the actual term, this exercise has the learner develop the key properties of the midsegment of a triangle. This task leads the class to discover a proof of similar triangles using the properties of parallel...

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

Learners observe and solve examples of corresponding angle postulates, alternate interior angle theorems, and exterior and consecutive angles. They complete the Determining Angle Measure With Parallel Lines worksheet.

Can you prove it? Lead your class through the development of the Side Splitter Theorem through proofs. Individuals connect the ratio and parallel method of dilation through an exploration of two proofs. After completing the proofs,...

Students identify similar triangles.  For this proportional segments lesson, students identify corresponding sides, set up ratios, and find the length of the missing side of a triangle.  They use the parallel/proportionality...

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...

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...

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...

You've investigated relationships between chords, radii, and diameters—now it's time for arcs. Learners investigate relationships between arcs and chords. Learners then prove that congruent chords have congruent arcs, congruent arcs have...

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...

Students investigate the usage of parallel and perpendicular shapes in the real world. In this geometry lesson, students investigate shapes for properties that are related to the real world. They relate all the properties of shape tot he...

Learners separate things that just appear similar from those that are actually similar. A diagram of triangles is given, and then a variety of geometric characteristics changed and the similarity of the triangles analyzed. Because the...

Given a pair of parallel lines and a triangle in between, geometers prove that the sum of the interior angles is 180 degrees. This quick quest can be used as a pop quiz or exit ticket for your geometry class.

A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...

So many times the characteristics of triangles are presented as a vocabulary-type of lesson, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a...

Looking for a different approach to triangle congruence criteria? Employ transformations to determine congruent triangles. Learners list the transformations required to map one triangle to the next. They learn to identify congruence...

Learners classify triangles and make connections regarding angle measurements and attributes of acute, right, and obtuse triangles. They listen to teacher define and explain triangles. Everyone imagines a place where a broken wing for a...

Students analyze a drawing of a regular octagon inscribed in a circle to determine angle measures, using knowledge of properties of regular polygons and the sums of angles in various polygons to help solve the problem. They use...

Lead your class on an exciting journey through the world of math as they review geometry facts and solve for unknown angles. They learn how to use auxiliary lines and congruent angles to correctly complete each practice problem...