Question

in a rectangle, opposite sides are ____ which means ___ congruent to ____. Triangles ABC and CDA can be proven congruent by hypotenuse-Leg because ___ is the hypotenuse for both triangles.

Answer 1

In a rectangle, opposite sides are parallel and congruent, meaning they are the same length. Right triangles within the rectangle can be proven congruent by the hypotenuse-leg theorem, where the Pythagorean theorem is used to relate the legs of a right triangle with the hypotenuse.

Step-by-step explanation:

In a rectangle, opposite sides are parallel which means they are congruent to each other. This means that each pair of opposite sides have the same length. Considering triangles ABC and CDA, if we presuppose that this rectangle has a right angle and hence can have a pair of right triangles, then we can use the hypotenuse-leg theorem to prove congruence between these triangles.

For right triangles, the hypotenuse is the longest side, opposite the right angle, and it would be the same for both triangles in our case. Using the Pythagorean theorem, which relates the lengths of the legs of a right triangle with the hypotenuse, we have the equation a² + b² = c², where c represents the length of the hypotenuse and a and b represent the lengths of the other two sides. Therefore, for both triangles ABC and CDA, the side that is the hypotenuse for both triangles is the longest side of the rectangle.