How would the following triangle be classified? isosceles acute isosceles right scalene acute scalene right
The Correct Answer and Explanation is:
The correct classification of the triangle is isosceles right.
This classification is based on two key observations from the image: the triangle has one 90-degree angle, as indicated by the square in the corner, and it has two sides marked as congruent. A right triangle is any triangle that contains one angle of exactly 90 degrees. An isosceles triangle has exactly two sides that are the same length. When these features appear together in a single triangle, the shape is called an isosceles right triangle.
This type of triangle is unique because its angles and sides follow a specific pattern. The two congruent legs meet at the right angle, and the third side, called the hypotenuse, is the side opposite the right angle and is longer than the other two. Because of the isosceles property, the two base angles opposite the congruent sides are equal, and since the angles of a triangle must sum to 180 degrees, those two angles must each measure 45 degrees. So, the angles of an isosceles right triangle are 45°, 45°, and 90°, and the side proportions follow a predictable ratio of 1:1:√2 if scaled accordingly.
The incorrect options can now be ruled out. A scalene triangle has no equal sides, so both scalene options are eliminated by the presence of two equal sides. An acute triangle has all angles less than 90 degrees, but this triangle contains a right angle. That rules out isosceles acute as well.
Therefore, the triangle shown is classified as isosceles right because it has one right angle and two equal-length sides. This type of triangle often appears in geometry problems, trigonometry, and architectural design for its symmetry and predictable properties.
