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...
Illustrative Mathematics
Are They Similar?
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...
Illustrative Mathematics
A Midpoint Miracle
Young geometers develop one of the fundamental properties of quadrilaterals (connecting side midpoints gives a parallelogram) in this short but thought-provoking exercise. Using a combination of hands-on techniques and abstract algebraic...
Illustrative Mathematics
Dilating a Line
High School geometers verify through experimentation certain properties about dilations. This multi-step problem challenges them to construct examples of dilations to verify specific facts, the final step provides an opportunity to more...
Illustrative Mathematics
Right Triangles Inscribed in Circles II
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...
Illustrative Mathematics
What Shape Am I?
Sharpen your pencil and grab a ruler, it's time to draw some quadrilaterals! Given the definition of a parallelogram, rectangle, and rhombus, learners draw examples and nonexamples of each figure. The three definitions are...
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 students to frame their responses.
Curated OER
Reflecting Reflections
A triangle rests in quadrant two, from which your class members must draw reflections, both over x=2 and x=-2. This focused exercise strengthens learners' skills when it comes to reflection on the coordinate plane.
5280 Math
Triangle Area Patterns
Combine algebraic and geometric strategies to find solutions. The task asks learners to find the coordinates of a third vertex of a triangle to create a triangle with a specific area. The project is a set of seven problems that...
Texas Instruments
Texas Instruments: Properties of Parallel Lines With Cabri Jr.
Cabri Jr. activity to study the properties of parallel lines.
Texas Instruments
Texas Instruments: Properties of Parallel Lines Cut by a Transversal
In this activity, students create parallel lines and a transversal, and study the properties of the lines and their angles.
Oswego City School District
Regents Exam Prep Center: Locus Equidistant From Two Parallel Lines
Use this site to learn about the fourth locus theorem regarding parallel lines. Click on the "Topic Index" link to find related practice activities and resources.
Texas Instruments
Texas Instruments: Mc Dougal Littell Geometry: Investigate Slopes
Students can use the TI-84 Plus family with Cabri Jr. to investigate properties of parallel lines.
Northeast Parallel Architectures Center, Syracuse University
Syracuse University: Properties of Absolute Value
This site by the Northeast Parallel Architecture Center, Syracuse University, reveals the secrets to solving problems that involve absolute value.
Oswego City School District
Regents Exam Prep Center: What Is a Locus?
This site defines what a locus is and offers links to five locus theorems. Walks you through the six "Steps to solving a locus problem."
Oswego City School District
Regents Exam Prep Center: Compound Locus
Loci are applied to word problems in this online tutorial. Practice problems are included. The teacher resource page supplies practical problems.