Virginia Department of Education
Circles in the Coordinate Plane
Make the connection between the distance formula and the equation of a circle. The teacher presents a lesson on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the coordinate plane and...
EngageNY
Unknown Area Problems on the Coordinate Plane
Scholars determine distances on the coordinate plane to find areas. The instructional activity begins with a proof of the formula for the area of a parallelogram using the coordinate plane. Pupils use the coordinate plane to determine...
Illustrative Mathematics
Similar Triangles
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...
Curated OER
Getting It Right! An Investigation of the Pythagorean Theorem
Learners construct a variety of right triangles using a right-angled set square, cutting corners from pieces of paper or cardboard, and using dynamic geometry software. They measure the sides of these various right triangles and record...
Illustrative Mathematics
Why Does SSS Work?
While it may seem incredibly obvious to the geometry student that congruent sides make congruent triangles, the proving of this by definition actually takes a bit of work. This exercise steps the class through this kind of proof by...
Curated OER
Coordinate Proofs
Students explore the concept of coordinate proofs. In this coordinate proofs lesson, students write coordinate proofs using properties of distance, slope, and midpoint. Students discuss why it is sometimes beneficial to double the...
EngageNY
Analytic Proofs of Theorems Previously Proved by Synthetic Means
Prove theorems through an analysis. Learners find the midpoint of each side of a triangle, draw the medians, and find the centroid. They then examine the location of the centroid on each median discovering there is a 1:2 relationship....
Curated OER
Which Quadrilateral Is It?
Students prove conjectures about geometric figures on the plane or in space using coordinate geometry. They develop fluency in operations with real numbers, vectors and matrices using mental computation or paper-and-pencil calculations...
Curated OER
Crystals: Geometry and Groups
Students discuss the importance of examining crystals and experiment growing them. In groups, they complete a project in which they use groups in geometry just like crystallographers. They practice solving the groups and proofs and...
EngageNY
Criterion for Perpendicularity
The Pythagorean Theorem is a geometry pupil's best friend! Learners explain the equation a1b1 + a2b2 = 0 for perpendicular segments using the Pythagorean Theorem. They are able to identify perpendicular segments using their...
EngageNY
How Do Dilations Map Segments?
Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions.
Curated OER
Tessellations: Geometry and Symmetry
Young scholars explore the concept of tessellations. In this tessellations lesson, students use an applet to construct tessellations. Young scholars use regular polygons to construct tessellations. Students find patterns and symmetry in...
EngageNY
Applications of the Pythagorean Theorem
Examine the application of the Pythagorean Theorem in problem-solving questions. Pupils apply the theorem to find lengths when given different scenarios. They finish the 17th installment in an 18-part series by applying the theorem...
Curated OER
Special Segments in a Triangle
In this geometry worksheet, 10th graders review the vocabulary associated with the special segments of a triangle and the associated points of concurrency and solve problems in which they find the indicated missing angle or...
Curated OER
Properties of Parallelograms
Students identify different properties of parallelograms. In this geometry lesson, students complete problems that proves the theorems and properties of parallelograms. They graph the different shapes on paper.
Curated OER
Profitable Soda Stand
Am I making any money? Help learners determine if their fictitious soda stand is turning a profit. They graph linear equations using the slope and y-intercept and identify the best price to use to sell soda. They identify the domain and...
Curated OER
Distance Formula
Students calculate the distance between two points using the distance formula. In this geometry lesson, students derive the distance formula using the Pythagorean Theorem.
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...
Virginia Department of Education
Similar Triangles
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...
Curated OER
Iterating Linear Functions
Students use a spreadsheet to investigate data. In this algebra lesson, students collect and graph data on a coordinate plane. They explain properties of a linear equation both algebraically and orally.
Curated OER
Got Complements? with Cabri Jr.
Learners use the axes and measure angle tool to explore and calculate complementary angles with Cabri Jr. They also identify what happens to the calculation as they drag the endpoint into a different quadrant. Finally, they label each...
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...
Curated OER
Interactivate - Lines, Rays, Line Segments, and Planes
Students explore lines, rays, line segments, and planes. In this math instructional activity, students discuss the math concepts and direct their instructor in graphing functions. Students collaborate in graphing additional functions.
Curated OER
Picking Pythagoras
Students discover that side measurement is used in determining angle classification of a triangle. By squaring sides, they predict whether triangles be right, obtuse, or acute. They prove the Pythagorean Theorem and use it to solve...