Questions: Find the values of x and y that make these triangles congruent by HL. x-3, y=4 x-5, y=6 x=6, y=5 x=4, y=3

Find the values of x and y that make these triangles congruent by HL. x-3, y=4 x-5, y=6 x=6, y=5 x=4, y=3
Transcript text: Find the values of $x$ and $y$ that make these triangles congruent by HL. $x-3, y=4$ $x-5, y=6$ $x=6, y=5$ $x=4, y=3$
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Solution

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Solution Steps

Step 1: Set up the equations

For the triangles to be congruent by HL (Hypotenuse-Leg), the hypotenuses and one leg must be congruent. We are given that the angles at B and E are right angles. Thus, segments BC and AE are legs and segments AC and AD are hypotenuses. We can set up the following equations:

  • x = y-1 (congruent legs)
  • 3x-2 = 2y+1 (congruent hypotenuses)
Step 2: Solve for x and y

Substitute the first equation (x = y-1) into the second equation:

3(y-1) - 2 = 2y + 1

3y - 3 - 2 = 2y + 1

3y - 5 = 2y + 1

y = 6

Now substitute y = 6 back into x = y - 1:

x = 6 - 1

x = 5

Final Answer

x = 5, y = 6

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