Triangle Exercises

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....

Is it possible to be the same yet different? Absolutely! The activity asks learners to explore the relationships between side ratios of triangles they have drawn. Because individuals all draw a triangle with the same angle measures, they...

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...

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...

Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....

Introduce your classes to a new world of mathematics. Pupils learn to call trigonometric ratios by their given names: sine, cosine, and tangent. They find ratios and use known ratios to discover missing sides of similar triangles. 

Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...

Start the exploration of trigonometry off right! Pupils build on their understanding of similarity in this lesson plan that introduces the three trigonometric ratios. They first learn to identify opposite and adjacent...

Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...

Middle and high schoolers solve fifteen problems from six exercise sets covering transformations, reflections, rotations, and enlargements. The solutions are provided.