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avatar+56 

I have this diagram. 

I know that PCQ = 45 Degrees and Angle C = 90 Degrees. 

 

I want to prove that AB^2 + BQ^2 = PQ^2. 

 

ugh.... I don't know what to do next. 

 

Help would be greatly appreciated fast :D

 Nov 11, 2020
edited by xCorrosive  Nov 11, 2020
 #1
avatar+111600 
+2

You cannot prove it because it is not true.  I assume you have written the question incorrectly.

 

 You want to prove that AB^2 + BQ^2 = PQ^2. 

 

But AB is bigger than PQ so the statement to be proven  is not true

 Nov 11, 2020
 #2
avatar+56 
0

Sorry about that!

I meant to say AP^2 + BQ^2 = PQ^2

xCorrosive  Nov 11, 2020
 #3
avatar+452 
+2

AC = BC = 5    |   ∠ACB = 90º    |    ∠PCQ = 45º    |    ∠ACP = ∠BCQ = 22.5º

 

Let M be a midpoint of AB

 

AB = sqrt (AC2 + BC2)

 

PQ = 2 * [tan(PCM) * CM]              ( CM = AM = BM )

 

AP = BQ = 1/2 (AB - PQ)

 

 Nov 11, 2020

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