Question

check all of the statements that are facts about triangles.

$a=\frac{1}{2}bh$

$a = bh$

three sided

interior angles have a sum of 180 degrees

interior angles have a sum of 360 degrees

every triangle has two names

every triangle has three names

all right triangles are isosceles

isosceles triangles have two congruent angles

equilateral triangles have three congruent sides and three congruent angles

Explanation:

• Area formula: The area formula for a triangle is \( A = \frac{1}{2}bh \) (not \( A=bh \), which is for a parallelogram).
• Definition: By definition, a triangle is a three - sided polygon.
• Angle sum: The sum of the interior angles of a triangle is \( 180^{\circ}\) (not \( 360^{\circ}\), which is for a quadrilateral).
• Naming: Triangles can be named by their side lengths (scalene, isosceles, equilateral) and by their angle measures (acute, right, obtuse), so every triangle has three names.
• Isosceles property: In an isosceles triangle, the angles opposite the equal sides are congruent.
• Equilateral property: An equilateral triangle has all three sides equal and all three angles equal (each \( 60^{\circ}\)).
• Right - isosceles relation: Not all right triangles are isosceles. A right triangle can be scalene (e.g., sides \(3,4,5\)).

Answer:

A. \( A=\frac{1}{2}bh \), C. Three sided, D. Interior angles have a sum of 180 degrees, G. Every triangle has three names, I. Isosceles triangles have two congruent angles, J. Equilateral triangles have three congruent sides and three congruent angles