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Serjik [45]
3 years ago
8

placing 12 tiles side by side, Pete can make a 12-by-1 rectangle. Name two other rectangles Pete can make with 12 tiles

Mathematics
1 answer:
sweet [91]3 years ago
6 0
6x2
3x4
.............................
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Question : In the given figure , ∆ APB and ∆ AQC are equilateral triangles. Prove that PC = BQ.
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Answer:

See Below.

Step-by-step explanation:

We are given that ΔAPB and ΔAQC are equilateral triangles.

And we want to prove that PC = BQ.

Since ΔAPB and ΔAQC are equilateral triangles, this means that:

PA\cong AB\cong BP\text{ and } QA\cong AC\cong CQ

Likewise:

\angle P\cong \angle PAB\cong \angle ABP\cong Q\cong \angle QAC\cong\angle ACQ

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Likewise:

m\angle QAB=m\angle QAC+m\angle BAC

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m\angle PAC=m\angle QAC+m\angle BAC

And by substitution:

m\angle PAC=m\angle QAB

Thus:

\angle PAC\cong \angle QAB

Then by SAS Congruence:

\Delta PAC\cong \Delta BAQ

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