EngageNY
Characteristics of Parallel Lines
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...
Radford University
Parallel Lines Cut by a Transversal
Use the parallel lines to find your way. After first reviewing geometric constructions and the relationships between angles formed by parallel lines and a transversal, young mathematicians write proofs for theorems relating to parallel...
Radford University
Parallel Lines, Transversals, and Angles: What’s the Connection?
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 apply...
EngageNY
Looking More Carefully at Parallel Lines
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...
Radford University
Parallel Lines Cut By a Transversal
Perhaps planning a city isn't so difficult after all. Scholars first perform geometric constructions and investigate how parallel lines are useful in real-world situations. They then work on a city design project, drawing street maps,...
Academic Magnet High School
Parallel Lines Proofs Practice
Here is a worksheet that lines up perfectly with the skills needed to finish a geometric proof. Eleven problems are given to see if learners can prove that lines are parallel or angles are congruent.
EngageNY
Informal Proofs of Properties of Dilations
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...
Virginia Department of Education
Lines and Angles
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...
Flipped Math
Proving Lines Parallel
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...
GeoGebra
Conjectures and Proof
Transform proofs using triangle rotations. By rotating a triangle around various points, class members develop proofs. Participants prove relationships of alternative interior angles formed by parallel lines and the sum of the interior...
Flipped Math
More with Proofs
Proofs may be as easy as 1, 2, 3 ... maybe. Pupils participate in creating four example proofs. The presentation uses a list of geometric properties to develop the proofs by filling in both the statements and reasons. Scholars practice...
Curated OER
Parallel and Perpendicular Lines
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 lines. ...
Illustrative Mathematics
Joining Two Midpoints of Sides of a Triangle
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 lines cut...
EngageNY
Unknown Angle Proofs—Proofs of Known Facts
Lead the class in a Greek history activity 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 practice...
Curated OER
Determining Angle Measure with Parallel Lines
Students 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.
Geometry Accelerated
Accelerated Geometry Review Sheet
Your geometry learners use their knowledge of various geometric concepts to write proofs. Starting with givens containing parallel line segments with transversals and triangles and quadrilaterals, and the mid-point and distance formulas;...
Curated OER
Parallel Lines
For this parallel lines worksheet, 10th graders solve and complete 16 different types of problems. First, they name the lines that are parallel to those listed. Then, students find that values that make each set of line parallel. They...
EngageNY
Congruence, Proof, and Constructions
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 is broken...
EngageNY
Comparing the Ratio Method with the Parallel Method
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,...
Curated OER
Semester 1 Review for Geometry final
In this geometry instructional activity, 10th graders solve problems that are based on the topics covered in a first semester geometry class, including, linear equations and the equations of parallel and perpendicular lines, the logic of...
Education Development Center
Proof with Parallelogram Vertices
Geometric figures are perfect to use for proofs. Scholars prove conjectures about whether given points lie on a triangle and about midpoints. They use a provided dialogue among fictional learners to frame their responses.
Curated OER
Challenge: Skills and Applications Lesson 3.3
In this angle measures activity, students solve 9 short answer problems. Students find values for x and y given two parallel lines cut by a transversal. Students use alternate interior, supplementary, and exterior angles to find x and y.
University of Utah
Geometry: Angles, Triangles, and Distance
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.
Curated OER
Proportional Segments Between Parallel Lines
Students identify similar triangles. In 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 conjecture to...