1 Answer

Faran · Answer 1 · 2021-10-17T02:13:40+0000

In both cases, you have to work on the angle between the sides you found out to be equal.

Diagram 1:

You can show that the angle PCB is the same as ACR. To prove this, you can think of angles:

$P\hat{C}B=P\hat{C}A + A\hat{C}B$

and

$A\hat{C}R=B\hat{C}R+A\hat{C}B$

So, angle
$A\hat{C}B$ is common, and both
$P\hat{C}A$ and
$B\hat{C}R$ are right angles.

So, angles PCB and ACR are both 90° plus a common term (ACB), and thus they're equal.

Diagram 2:

We will work very similarly here: in this case, you have

$A\hat{B}G = A\hat{B}C-G\hat{B}C$

and

$C\hat{B}E=G\hat{B}E-G\hat{B}C$

Again, both
$A\hat{B}C$ and
$G\hat{B}E$ are right angles, so we have

$A\hat{B}G = 90-G\hat{B}C$

and

$C\hat{B}E=90-G\hat{B}C$

So, both
$A\hat{B}G$ and
$C\hat{B}E$ are 90 minus a common term, so they are equal.

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