Question

Given: abcd is a rectangle. prove: abcd has congruent diagonals. identify the steps that complete the proof.

Answer 1

parallel side theorem 
SAS
CPCTC

Answer 2

In this question we have to proof ABCD has congruent diagonal. By SAS property and reflexive property we will be proved as follows:

Given:

ABCD is a rectangle.

Prove:

Diagonal AC ≅ Diagonal BD

According to question,

As we know that, ABCD is a rectangle, it is also a parallelogram.

Thus, ABCD is a parallelogram, opposite sides of a parallelogram are congruent.

⇒ AB ≅  DC  

⇒ BC ≅ BC (Reflexive Property of Congruence)

Hence, ∠ABC and ∠DCB are right angles by the definition of rectangle.

∠ABC ≅ ∠DCB (all right angles are congruent)

Therefore, by SAS property, $\Delta$ ABC ≅ $\Delta$ DCB.

⇒ segment AC ≅ segment BD

Hence proved

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