Question

Model Sketch a square and sketch an equilateral triangle. Draw a diagonal of the square to divide the square into two congruent right triangles. Then draw a segment in the equilateral triangle that divides it into two congruent right triangles. In all four right triangles, write each angle measure.

Answer 1

A square divided by a diagonal creates two congruent right triangles with angles of 90 degrees, 45 degrees, and 45 degrees. An equilateral triangle divided by a segment from a vertex to the midpoint of the opposite side creates two congruent right triangles with angles of 90 degrees, 60 degrees, and 30 degrees. Each right triangle has one right angle, and their other angles depend on the originating shapes.

Step-by-step explanation:

To start, sketch a square. All sides of a square are equal and its angles are all 90 degrees.

By drawing a diagonal from one corner to the opposite corner, you will divide the square into two congruent right triangles.

In these triangles, the angles will be 90 degrees, 45 degrees, and 45 degrees, because the diagonal cuts the 90-degree angle of the square in half, and the other two angles remain 45 degrees as in any right-angled isosceles triangle.

Next, sketch an equilateral triangle.

All sides and angles are equal in an equilateral triangle, and the angles each measure 60 degrees.

To divide it into two congruent right triangles, you draw a line from one vertex to the middle of the opposite side, thereby creating two 30-60-90 triangles.

In these triangles, the right angle measures 90 degrees, one angle measures 60 degrees (the angle from the original equilateral triangle), and the last angle measures 30 degrees.

In summary, after dividing both shapes, all four right triangles have one angle measuring 90 degrees, and the remaining angles will depend on the properties of the originating shape (45 degrees for the square's right triangles, and 60 and 30 degrees for the equilateral triangle's right triangles).