Answer with Always, Sometimes or Never True. Kindly explain why so that I can understand. Thanks.
1. An interior angle and an exterior angle of a triangle are supplementary.
2. The bisector of an angle of an isosceles triangle is also a perpendicular bisector.
3. The sum of two side lengths of a triangle is less than the length of the third side.
#1 is always true. Draw a triangle. Extend one side so that you can see the interior and exterior angles. They add up to a straight line (the extended side). Thus they are supplementary.
#2 sometimes
#3 never
Have you tried drawing the triangles to illustrate the ideas?
1. Always True.
An interior angle of a triangle and its corresponding exterior angle always add up to 180 degrees. This is known as the Exterior Angle Theorem.
2. Sometimes True.
The bisector of an angle of an isosceles triangle can be a perpendicular bisector if the isosceles triangle is also a right triangle. In this case, one of the angles is 90 degrees, and the bisector will be perpendicular to the side opposite the right angle. However, if the isosceles triangle is not a right triangle, then its bisector will not be a perpendicular bisector.
3. Always True.
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This is known as the Triangle Inequality Theorem. If the sum of the lengths of two sides is equal to or less than the length of the third side, it would not be possible to form a closed figure, violating the basic definition of a triangle.