Question

A triangle has two 90° angles and a side 12 centimeters in length. Select True or False for each statement about this type of triangle.

1. No such triangle is possible. True or False?
2. The triangle must be a right triangle. True or False?
3. The third angle must be 90°. True or False?

Answer 1

It is impossible for a triangle to have two 90-degree angles as this would exceed the total 180 degrees allowable for a triangle's internal angles. Thus, the first statement is true, and the second and third statements are false.

Step-by-step explanation:

Understanding Triangles and Angles

When analyzing the properties of a triangle, it's important to remember that a triangle is a three-sided polygon where the sum of the internal angles is always 180 degrees. Given the facts about triangles:

1. No such triangle is possible. True. A triangle cannot have two 90° angles because adding a third angle would exceed the total sum of 180° for a triangle.
2. The triangle must be a right triangle. False. A right triangle can only have one angle of 90°, which accounts for half of the total angle sum, and the other two angles must add up to the remaining 90°.
3. The third angle must be 90°. False. As stated above, the third angle in a triangle cannot be 90° if the other two angles are already 90° each since the total would sum up to 270°, which is not possible for a triangle.

This aligns with the fundamental definition that the sum of all internal angles in a triangle must equal 180 degrees.