EngageNY
Properties of Parallelograms
Everyone knows that opposite sides of a parallelogram are congruent, but can you prove it? Challenge pupils to use triangle congruence to prove properties of quadrilaterals. Learners complete formal two-column proofs before moving on to...
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.
CK-12 Foundation
Parallelogram Proofs: Quadrilaterals that are Parallelograms
What conditions must be met for a quadrilateral to be a parallelogram? A slider interactive allows individuals to move the vertices of a quadrilateral. They answer questions that prove whether a given quadrilateral is a parallelogram.
Radford University
Triangles in Parallelograms
What's the point of looking at triangles when trying to draw parallelograms? Given three non-collinear points, pupils determine and justify all possible points that would create a parallelogram. They then analyze the four triangles that...
West Contra Costa Unified School District
The Parallelogram Law
Use your pupils' sense of curiosity to explore the Parallelogram Law. Here is an activity that outlines a complete lesson from beginning to end, allowing pupils to follow a conjecture through to the proof stage.
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....
Inside Mathematics
Quadrilaterals
What figure is formed by connecting the midpoints of the sides of a quadrilateral? The geometry assessment task has class members work through the process of determining the figure inscribed in a quadrilateral. Pupils use geometric...
Curated OER
Properties of Parallelograms
Young scholars 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
Parallelograms
In this parallelograms worksheet, 10th graders identify and describe a quadrilateral, a diagonal, and a parallelogram in 7 different problems. First, they find the values of x, y, and z in each quadrilateral to prove that it is a...
Curated OER
Tests for Parallelograms
In this tests for parallelograms learning exercise, 10th graders solve 7 various types of geometry problems that include parallelograms. First, they determine if each quadrilateral is a parallelogram and justify their answers. Then,...
Curated OER
Parallelograms
In this parallelograms worksheet, 10th graders solve 8 different types of problems related to measuring various parallelograms. First, they use the figure, a parallelogram, illustrated at the top to solve each problem. Then, students...
Curated OER
Midpoints
In this midpoints instructional activity, 10th graders solve and complete 10 different problems. First, they find the perimeter of each illustrated triangle. Then, students determine the bases and median of a trapezoid. They also prove...
Curated OER
Area of Quadrilaterals
In this area of quadrilaterals worksheet, 10th graders solve and complete 5 various types of problems. First, they solve each of the triangles shown and find the area of each triangle. Then, students prove that the sum of the squares of...
Curated OER
Similarity
In this similarity worksheet, 10th graders solve and complete 14 different types of problems. First, they find the length of each segment given two lines parallel. Then, students find the measure of each segment of a parallelogram...
Curated OER
Application of Properties of Quadrilaterals in the Coordinate Plane
Students apply definitions and theorems to verify special quadrilaterals
using coordinate geometry. They apply the slope formula, the midpoint
formula, and the distance formula to justify that a given quadrilateral is a
parallelogram....
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...
Mathematics Assessment Project
Floor Pattern
You'll never look at floor tiles the same again. An assessment task prompts learners to investigate relationships between patterns involving squares and kites to determine angle measurements. They then prove whether a given quadrilateral...
Key Curriculum Press
Properties of Special Parallelograms
Rhombuses, rectangles and squares are have special properties. In this lesson, young geometers investigate and make conjectures about diagonals, angles, and parallel lines of parallelograms.
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
Coordinate Geometry Proofs
In this coordinate geometry worksheet, 10th graders solve and draw 10 different problems related to complete proofs in coordinate geometry. First, they prove that a figure with given points is another figure by using slopes. Then,...
Curated OER
Similarity
In this similarity worksheet, 10th graders solve and complete 14 different types of problems. First, they refer to each drawn figure given that the lines are parallel. Then, students find the length of each segment listed. In addition,...
Jesuit High School
Geometry Sample Problems
I'd like to prove that this worksheet has a lot to offer. Seven problems using triangles and parallelograms practice the traditional method of a two-column proof. After the worksheet is some practice problems that show worked out...
Curated OER
Connecting Algebra and Geometry Through Coordinates
This unit on connecting algebra and geometry covers a number of topics including worksheets on the distance formula, finding the perimeter and area of polynomials, the slope formula, parallel and perpendicular lines, parallelograms,...
Illustrative Mathematics
Right Triangles Inscribed in Circles II
So many times the characteristics of triangles are presented as a vocabulary-type of activity, 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...