Question

Given any kind of triangle, you can find its side lengths by applying the Pythagorean Theorem for right triangles, depending on what information you’re given. You will use GeoGebra to see how the Pythagorean Theorem can be used to solve non-right triangles. If you are not able to use GeoGebra, I will provide a picture of the triangle below. Go to right triangles and the Pythagorean Theorem and complete each step below.

Create a line through point B perpendicular to line AC and label the intersection of the perpendicular line and line AC point D. Measure and record BD and m∠BDA. What do you know about ∆ABD and ∆BCD based on their angle measurements?
a) ∆ABD is congruent to ∆BCD
b) ∆ABD is similar to ∆BCD
c) ∆ABD and ∆BCD have equal areas
d) ∆ABD and ∆BCD are not related by angle measurements

Answer 1

Two triangles formed by drawing a line perpendicular from point B to line AC are similar if they share a right angle and another equal angle. The Pythagorean Theorem states that in a right triangle with legs a and b, and hypotenuse c, the relationship between the sides is a² + b² = c². This theorem is utilized to calculate the sides of right triangles.

Step-by-step explanation:

The question involves understanding how the Pythagorean Theorem can be used to determine the lengths of sides within triangles, specifically right triangles. When a line is drawn through point B perpendicular to line AC, intersecting at point D, what is formed are two right-angled triangles, ∆ABD and ∆BCD. By measuring BD and m∠BDA, we can understand the relationship between the triangles. Knowing that both triangles have a right angle, and if they share another equal angle, they are similar triangles because they will have all their angles in the same proportion. However, without further information about their sides, we cannot claim they are congruent.