Area of a Triangle

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....

Under which conditions can a triangle be classified as isosceles? High schoolers practice identifying isosceles triangles and special line segments, including angle bisectors, medians of triangles, and perpendicular bisectors of sides of...

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...

Explaining the distance formula as "an application of the Pythagorean Theorem" might relieve some of your young mathematicians who are scratching their head at all the new concepts. Sal demonstrates how to take the distance between any...

45-45-90 triangles are half a square, which gives them a special status! The instructor explains the relationship of the sides of the 45-45-90 triangle using the Pythagorean Theorem as a reference. 

The isosceles triangle comes with its own set of properties. A lecturer shows how to apply the Isosceles Triangle Theorem to find missing side lengths or angle measures. The final example involves both square roots and quadratic equations. 

While the instructional activity focuses on right triangles, this activity offers a great way to practice the area of all triangles through an interactive webpage. The activity begins with the class taking a square paper and cutting in...

A trigonometric ratio is a ratio between two sides of a right triangle. In this problem, find sin(A) in the given right triangle. Use the ratio of the opposite side over the hypotenuse.

The shortest distance between two points is a straight line. Learners use the Pythagorean Theorem to develop a formula to find that distance. They then find the midpoint using an average formula.