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Yakvenalex [24]
2 years ago
12

Given: ABCD is a rectangle.

Mathematics
2 answers:
oee [108]2 years ago
8 0

By SAS property, ABC ≅  DCB.

<h3>How to prove the deductions</h3>

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

Given:

ABCD is a rectangle.

Prove:

Diagonal AC ≅ Diagonal BD

From the question,

As we can see 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,  ABC ≅  DCB.

⇒ segment AC ≅ segment BD

Learn more about rectangular congruency here:

brainly.com/question/7162498

#SPJ1

Savatey [412]2 years ago
8 0

Answer:

♣ = <u><em>parallelogram side theorem</em></u>

♦ = <u><em>SAS</em></u>

♠ = <u><em>CPCTC</em></u>

(Correct On Edgen)

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