Triangles and Congruence

Here the focus is on triangle congruence. Through an activity that requires investigation, questioning, and working together, geometers learn to identify corresponding parts of triangles to determine if the triangles are congruent....

Show your school spirit while proving theorems about triangles! Your student geometers are charged with coming up with a new design for the school pennant, following specific guidelines. Along the way, they need to prove the theorem that...

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...

What do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find...

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...

Rigid motions are to congruence as what are to similarity? Investigate properties of rigid motions and define congruence in terms of rigid motions with the ninth chapter of a 10-part eighth grade workbook series. The lesson then prompts...

Corresponding parts, congruent parts, congruent corresponding parts—what does it all mean? The resource challenges pupils to identify corresponding parts for pairs of figures. It uses examples of figures that undergo rigid...

Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...

Try five problems on triangles. Levels A and B focus on shapes that can be created from right triangles. Level C touches upon the relationship between the area of a six-pointed star and the area of each triangle of which it is composed....