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.
6th Grade Math - Triangles Lesson