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ella [17]
3 years ago
6

GIVEN: ab perpendicular to BC AND DC PERPENDICULAR TO BCAC = BDPROVE:AB =DC Proofs

Mathematics
2 answers:
Ad libitum [116K]3 years ago
6 0

Answer with Step-by-step explanation:

We are given that AB is perpendicular to BC and DC perpendicular to BC.

AC=BD

We have to prove that AB=DC

In triangle ABC and triangle DCB

AC=BD  (Given)

\angle B=\angle C=90^{\circ}

BC=BC

Reason:Reflexive property

\triangle ABC\cong \triangle DCB

Reason:RHL postulate

AB\cong DC

Reason:CPCT

Therefore, AB=DC when two sides are congruent then the sides are equal.

Hence, proved.

Aleonysh [2.5K]3 years ago
5 0
Let's take a look at the triangles ABC and DCB

1. angles : B=C=90° because they are right triangles (AB perpendicular to BC and DC perpendicular to BC)

2. AC=BD (given)
3. BC is in common (the two triangles have it, you can say it like BC=BC)

So we proved that by SAS(side angle side), the triangles are congruent ABC= DCB

Since the triangles are congrueny, all their sides are equal so we can say that AB=DC
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