Curated OER
Geometry Project
Proofs are usually an intimidating assignment. An engaging lesson focused on geometric proofs may reduce the anxiety! Pupils choose between several triangle proofs to complete and work on completing them. The...
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
Triangle's Interior Angles
Given a pair of parallel lines and a triangle in between, geometers prove that the sum of the interior angles is 180 degrees. This quick quest can be used as a pop quiz or exit ticket for your geometry class.
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...
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.
Illustrative Mathematics
Placing a Fire Hydrant
Triangle centers and the segments that create them easily become an exercise in memorization, without the help of engaging applications like this lesson. Here the class investigates the measure of center that is equidistant to the three...
Illustrative Mathematics
Equal Area Triangles on the Same Base II
A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...
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...
Illustrative Mathematics
Reflections and Isosceles Triangles
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...
Illustrative Mathematics
Tangent to a Circle From a Point
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...
Maths Challenge
Maths challenge.net: Circumscribed Triangle
Find the area of this circumscribed triangle with your geometry skills.
Maths Challenge
Maths challenge.net: Triangle Area
Find the area of this triangle in a coordinate plane.
Maths Challenge
Maths challenge.net: Right Triangle Equal Parts
A geometry proof problem involving a right triangle and finding angles of equal measure.
Maths Challenge
Maths challenge.net: Tick Tock Triangle
This is a "three star" geometry problem where prior knowledge of probability is required to solve this "Tick Tock Triangle" problem, have fun!
Maths Challenge
Maths challenge.net: Triangle in a Square
A "three star" geometry problem requiring some prior knowledge in math and proofs to maximize the area of an inscribed triangle in terms of the hypotenuse.
Maths Challenge
Maths challenge.net: Shaded Triangle
A great geometry problem of area, encorperating many learned skills.
Maths Challenge
Maths challenge.net: Maximum Square
A challenging proof like geometry of finding the square inscribed in a triangle.
Maths Challenge
Maths challenge.net: Right Angle Reasoning
A geometry problem for students to use their mathematical reasoning skills to explain a right triangle property.
Maths Challenge
Maths challenge.net: Measuring Mountains
Use your triangle solving skills to solve this triangle problem and then apply it to the real world.
Maths Challenge
Maths challenge.net: Leaning Ladders
Use your right triangle solving skills to solve this ladders in a hole problem.
Maths Challenge
Maths challenge.net: Perpendicular Construction
This is a "three star" geometry problem where prior math problem skills and proof experience is recommended to solve this "Perpendicular Construction" problem.
Maths Challenge
Maths challenge.net: Tri Angles
A geometry proof involving exterior angles of a triangle.
Maths Challenge
Maths challenge.net: Corner Circle
This is a "three star" geometry problem where prior knowledge of circles and triangles is recommended to solve this circle in the corner problem.
Maths Challenge
Maths challenge.net: Shaded Hexagon
A problem with equilateral triangles and area to solve this "Shaded Hexagon" problem. Mathematical reasoning and triangle knowledge will be needed to solve the problem.