3 years ago

PLZ HELP!!!!!! (WILL GIVE BRAINLIEST!!!!)

Mathematics

1 answer:

sdas [7]3 years ago

8 0

A. yes
B. yes
C. no
D. yes
E. no

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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:

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

Since they all measure 60°.

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Since ∠QAC ≅ ∠PAB:

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

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$m\angle PAC=m\angle QAB$

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$\angle PAC\cong \angle QAB$

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$\Delta PAC\cong \Delta BAQ$

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$PC\cong BQ$

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