TRIANGLES

The sum of the measures of the angles of a triangle is 180°.

Find the sum of each set of angles.

14° + 46° + 110° = 170°

14° + 32° + 134° = 180°

The sum of the first set of angles is 170°.

So, those three angles could not be the three angles of a triangle.

The sum of the second set of angles is 180°.

So, those three angles could be the three angles of a triangle.

The shortest side of a triangle is always opposite the smallest interior angle.

The longest side of a triangle is always opposite the largest interior angle.

The shortest side is AB. So, the smallest angle is ∠*C*.

The longest side is AC. So, the largest angle is ∠*B*.

Therefore, the angles in order from largest to smallest are: ∠*B*, ∠*A*, ∠*C*.

The largest angle is ∠*Y*. So, the longest side is XZ.

The smallest angle is ∠*Z*. So, the shortest side is XY.

Therefore, the sides in order from longest to shortest are: XZ, YZ, XY.

The sum of the lengths of any two sides of a triangle

is greater than the length of the third side.

Check the sums to see if the side lengths can be formed into a triangle.

The sum of 2 feet and 7 feet is 9 feet, which is greater than 4 feet.

The sum of 4 feet and 7 feet is 11 feet, which is greater than 2 feet.

The sum of 2 feet and 4 feet is 6 feet, which is less than 7 feet.

Since not all of the sums are greater than their respective third sides, the side lengths cannot be formed into a triangle.