Final answer:
In a rectangle, opposite sides are congruent. For triangle congruence, the hypotenuse used in hypotenuse-leg can be AC in a rectangle, if the rectangle is a square. However, using hypotenuse-leg theorem is not typically standard for proving congruence of triangles in a rectangle unless it is also a square.
option d is the correct
Step-by-step explanation:
To fill in the blanks for the student's question regarding a rectangle and triangle congruence:
- In a rectangle, opposite sides are congruent which means they are exactly the same in terms of shape and size.
- Triangles ABC and CDA can be proved congruent by hypotenuse-leg because AC (Blank 2 option) is the hypotenuse for both triangles, and the leg (side) shared by both triangles is the same.
- The hypothesized congruence would not typically be proven using hypotenuse-leg, since this applies to right triangles and a rectangle doesn't have to contain right triangles unless it is a square. However, when dissecting a rectangle into triangles, leg AB of triangle ABC and leg CD of triangle CDA are also congruent, just as BC and DA (Blank 3 options) are.
- Since rectangles typically do not consist of right triangles unless they are squares, the hypothesis of proving two triangles in a rectangle congruent using hypotenuse-leg is not standard. But for any right triangles derived from a rectangle, if we assume these are right triangles, the hypotenuse shared would be AC (Blank 4 option).
Note, the use of hypotenuse-leg theorem is typically reserved for right triangles, and a rectangle will only have right triangles if it is a square. In a rectangle, the diagonals are congruent but not normally referred to as hypotenuses unless the rectangle is also a square.