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What values of b and c make WXY congruent to FEG in

What values of b and c make WXY congruent to FEG in-example-1
User Gadicc
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1 Answer

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The Hypotenuse-Leg Theorem states that two right triangles are congruent if and only if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of the other right triangle.

From this theorem, we know that corresponding sides must be equal for those triangles to be congruent. Then, we get two equations


\begin{gathered} c-2=2c-22 \\ 4b+18=b+48 \end{gathered}

Let's start solving the equation for b.


4b+18=b+48

We can start by subtracting 18 from both sides of the equation


\begin{gathered} 4b+18-18=b+48-18 \\ 4b=b+30 \end{gathered}

Now, we can subtract b from both sides.


\begin{gathered} 4b-b=b+30-b \\ (4-1)b=30 \\ 3b=30 \end{gathered}

And finally, dividing both sides by 3 we have


\begin{gathered} (3b)/(3)=(30)/(3) \\ b=10 \end{gathered}

Now we have our b value. b = 10. Now, let's calculate the value for c.


c-2=2c-22

We can start by adding 22 to both sides of the equation


\begin{gathered} c-2+22=2c-22+22 \\ c+20=2c \end{gathered}

Now, we can just subtract c from both sides to get our value


\begin{gathered} c+20-c=2c-c \\ 20=(2-1)c \\ c=20 \end{gathered}

Then, we have our c value, c = 20.

User Guthrie
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