Give two sets of potential sides for a triangle. one set of side lengths should be able to be used for a right triangle and the other set of side lengths should not be able to form a right triangle.

suppose you’re making a triangle where you know the measures of two angles and the length of the side between those two angles. write to angle measures and the length of the side between them for your triangle. you can use any measurements you want as long as they could really be used to form a triangle.

Problem 1:

Set one: 5, 12, 13

Set two: 4, 9, 12

Notice that the first triangle satisfies Pythagorean theorem:

     5^2 + 12^2 = 13^2

     25 + 144 = 169

     169 = 169, so it is a right triangle.

The second triangle does not follow Pythagorean theorem so it is not a right triangle.

Problem 2:

angle 1: 30°
angle 2: 60°
length of the side between the two angles: 25

Notice that the other sides are determined.

When you draw a segment with length 25, and then add two lines, one from each end of the given segment, one of the lines with angle 30° and the other one with angle 60°, the two lines will intersect each other forming a triangle.

The tirangle given is unique and you can check wheter it is rigth or not.