101 Questions
Best Reflection
Which is the best reflection of them all? Given four diagrams, pupils determine which one shows the most accurate reflection of a quadrilateral. Two images provide the distances of each vertex from the line of reflection, as well as the...
Illustrative Mathematics
Points equidistant from two points in the plane
Young geometers apply their deductive reasoning skills and knowledge of proving triangles congruent in a task that asks them to prove if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints...
Curated OER
Unit Squares and Triangles
This is an interesting geometry problem. Given the figure, find the area of a triangle that is created by the intersecting lines. The solution requires one to use what he/she knows about coordinate geometry, as well as triangle...
Curated OER
Reflections and Equilateral Triangles
Your learners collaboratively find the lines of symmetry in an equilateral triangle using rigid transformations and symmetry. Through congruence proofs they show that they understand congruence in terms of rigid motions as they...
Curated OER
Inscribing a Square in a Circle
Inscribing a square in a circle brings up a number of interesting geometry topics including triangle congruence and how to prove a quadrilateral is a square. This activity is followed up by finding the area of the square and determining...
Illustrative Mathematics
Midpoints of the Sides of a Paralellogram
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...
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
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...
Texas Instruments
Texas Instruments: Finding the Shortest Path
Students discover the shortest distance light travels from an object to the human eye, as the light from the object reflects off a single mirror. In the process they learn about reflection in a line, congruent angles, angle bisectors,...
Oswego City School District
Regents Exam Prep Center: Copy a Line Segment and an Angle
This site provides a step-by-step method to construct congruent segments and angles with a straight edge and compass.
Texas Instruments
Texas Instruments: Perpendicular Bisector of a Line Segment
Students learn to draw a segment and its perpendicular bisector. They understand right angles and congruent segments. Students observe that changing the length or orientation of the segment changes the perpendicular bisector.
National Council of Teachers of Mathematics
Nctm: Illuminations: Diagonals to Quadrilaterals I
This resource explores the diagonals of quadrilaterals. The interactive tool allows learners to examine intersecting line segments in a variety of ways. Topics discussed are perpendicular diagonals, congruent diagonals, and bisected...
National Institute of Educational Technologies and Teacher Training (Spain)
Ministerio De Educacion: Flecha
Can you make the second arrow the same size as the first? You will be surprised.