Question

Given: The coordinates of rectangle DEFG are D(0, b), E(a, b), F(a, 0), and G(0, 0). Prove: The diagonals of a rectangle are congruent. As part of the proof, find the length of .

Answer 1

Answer:

The answer to your question is below

Step-by-step explanation:

Data

D (0, b)

E (a, b)

F(a, 0)

G (0, 0)

From this information, we conclude that the diagonals are EG and DF.

To prove that they are congruent we must calculate their length.

dEG = $\sqrt{(0- b)^{2} + (0 - a)^{2}}$

dEG = $\sqrt{b^{2} + a^{2}}$

dDF = $\sqrt{(a - 0)^{2} + (0 - b)^{2}}$

dDF = $\sqrt{a^{2} + b^{2}}$

Conclusion

The length of EG is equal to the length of DF, so they are congruent.