Question

Henry cuts a large triangle into three congruent triangles. Then he puts them together as shown. What geometric fact did Henry illustrate?

a) The sum of the measurements of the angles of a triangle always equals 180°
b) The angle of a triangle with the smallest measure is opposite the shortest side.
c) No more than one angle in a triangle can have a measurement greater than 90°
d) The length of any side of a triangle is shorter than the sum of the other two sides.

Answer 1

a) The sum of the measurements of the angles of a triangle always equals 180°.

Explanation:

Henry illustrated the geometric fact that the sum of the angles in any triangle is always equal to 180 degrees.

When he cut a large triangle into three congruent triangles and rearranged them, the total angles remained constant, demonstrating that regardless of how a triangle is divided or manipulated, the sum of its angles remains fixed at 180 degrees. This is a fundamental property of triangles in Euclidean geometry, known as the Triangle Sum Theorem.

Henry's action reinforced this theorem by revealing that even when the triangle's shape changes, the sum of its internal angles remains constant and adds up to 180 degrees. This principle is foundational in understanding the properties and relationships within triangles.