Develop a strong understanding of what it means to be a midpoint. Learners analyze the angles, coordinates, and lengths of segments and their approximated midpoints. They use their analyses to develop a formula to rank four attempts at...

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...

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...

This task asks learners to prove that the segment joining the midpoints of two sides of a parallelogram is both congruent and parallel to an adjacent side of the parallelogram. The activity would be good to use in a discussion about how...

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.

Have learners graph complex numbers to gain a visual and mathematical understanding of the distance and the midpoint between two complex numbers. This lesson is short, but to the point, and addresses an important complex number...

Challenge your classes while developing their problem-solving skills. A square is divided neatly into four equal triangles by its diagonals until one diagonal is moved from a vertex to the midpoint of one side. Now, scholars must devise...

In the ecological game of who eats who, one small change can have a big impact! Individuals create food chains in an array of ecosystems, then determine what happens to organisms in the chain when one organism changes its feeding...

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...

The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle...

Given the lines of symmetry in an equilateral triangle, your learners find where the pre-image vertices are mapped onto the new image. They explore the properties of equilateral triangles, the impact of reflections, and the...

Young geometers become pool sharks in this analysis of the angles and lengths of a trick shot. By using angles of incidence and reflection to develop similar triangles, learners plan the exact placement of balls to make the shot....

What can symmetry tell us about triangles? After looking at four examples, learners will come to realize that lines of symmetry are different for equilateral, isosceles, and scalene triangles. Use this guided practice activity as an...

Your algebra learners emphasize the"geometric" in geometric series as they use a common ratio between algebraic terms and find that it corresponds to a repeated similarity transformation. 

Learners explore mapping a rectangle onto itself using rigid motion concepts, geometric intuition and experimenting with manipulatives in a collaborative task.

Gaining practice in translating a verbal description into a diagram and then an equation is the real point of this similar triangles exercise. Once the diagram is drawn, multiple methods are provided to reach the conclusion. An effective...

Geometers explore symmetries of isosceles triangles by using rigid transformations of the plane. They complete four tasks, including congruence proofs, which illustrate the relationship between congruence and rigid transformations. The...

Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using...

In response to a student question, the "question corner" mentions two different methods to prove that the Midpoint Formula truly does work.

The Midpoint Formula finds the exact point that is halfway between two points. "Dr. Math" provides a formula that can be used to locate a point that is some fractional part of the entire segment.

This lesson from Purplemath demonstrates how to use the Midpoint Formula and shows typical problems using the Midpoint Formula.

Step by step instructions are given for the students to draw a segment, find the midpoint, and label the coordinates of the two endpoints and the midpoint. The students then record the data in a table for various segments. Based on the...

Twenty problems present a variety of problems working with various aspects of finding the midpoint of a line segment. They are given with each step to the solution cleverly revealed one at a time. You can work each step of the problem...

The purpose of the activity is for students to verify the results of the Midpoint Formula using the dynamic capabilities of Cabri Jr.