Questions: What values of x and y make triangle FGH congruent to triangle CDE? x= y=

What values of x and y make triangle FGH congruent to triangle CDE? x= y=
Transcript text: What values of $x$ and $y$ make $\triangle F G H \cong \triangle C D E$ ? \[ \begin{array}{l} x=\square \\ y=\square \end{array} \]
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Solution

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Solution Steps

Step 1: Set up the equations

Given that ΔFGH ≅ ΔCDE, we can set up the following equations based on corresponding sides:

  • FH = CE => x - 2y + 36 = 2x + y - 40
  • FG = CD => 2y + 9 = 4y - 29
  • GH = DE
Step 2: Solve for y

Using the second equation 2y + 9 = 4y - 29, we can solve for y: 2y - 4y = -29 - 9 -2y = -38 y = 19

Step 3: Solve for x

Substitute y = 19 into the first equation x - 2y + 36 = 2x + y - 40: x - 2(19) + 36 = 2x + 19 - 40 x - 38 + 36 = 2x - 21 x - 2 = 2x - 21 x - 2x = -21 + 2 -x = -19 x = 19

Final Answer:

x = 19 y = 19

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