Learn about constructing figures, proofs, and transformations. The seventh unit in a course of nine makes the connections between geometric constructions, congruence, and proofs. Scholars learn to construct special quadrilaterals,...

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...

Is this enough to show the two triangles are congruent? Small groups work through different combinations of constructing triangles from congruent parts to determine which combinations create only congruent triangles. Participants use the...

Your learners connect the new concepts of transformations in the coordinate plane to their previous knowledge using the solid vocabulary development in this unit. Like a foreign language, mathematics has its own set of vocabulary terms...

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...

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...

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...

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.

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...

Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...

Even U.S. President James Garfield had his own proof of the Pythagorean Theorem! Pupils consider three different attempts at a geometric proof of the Pythagorean Theorem. They then select the best proof and write paragraphs detailing...