2. The Pythagorean Theorem and Its Converse
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Recall the Converse of the Pythagorean Theorem and Pythagorean Inequalities Theorems. Find the measure of each side using the Distance Formula.
Type of Angle: Obtuse
Explanation: See solution.
Given the measures of all three sides of a triangle, we can determine whether it is right, acute, or obtuse by using the Converse of the Pythagorean Theorem and Pythagorean Inequalities Theorems. In each case, c is the length of the longest side.
Now, we can find the measure of each side using the Distance Formula.
Side | Distance Formula | Simplify |
---|---|---|
XY, ( 1,2), ( 4,6) | sqrt(( 4- 1)^2+( 6- 2)^2) | 5 |
YZ, ( 4,6), (6,6) | sqrt((6- 4)^2+(6- 6)^2) | 2 |
ZX, (6,6), ( 1,2) | sqrt(( 1-6)^2+( 2-6)^2) | sqrt(41) |