Question

Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.

Answer 1

The answer is (SAS) Theorem. Because  we know triangle ERT is congruent to  triangle CTR, it has the sides ( C& E and R&T, and the angle T&R).

Hope its correct.

Answer 2

Consider the triangles ERT and  CTR.

|ER|=|CT| shown

(Therefore, one can say that segment ER is congruent to segment CT.)

m(R)=m(T)= 90°shown

(By the definition of a rectangle, all four angles measure 90°)

|RT|=|TR|

so we have Side Angle Side congruence.

By the (SAS) Theorem, the triangles are congruent.


Answer: C (SAS) Theorem