Question

34 find the values of x and y that make these triangles congruent by the hl theorem. x = 2, y = 1 x = 3, y = 8 x = 3, y = 2 x = 8, y = 3

Explanation:

Step1: Set up equations based on HL Theorem

For the hypotenuse: \(3y + 1=x + 4\). For the leg: \(2y=x\).

Step2: Substitute \(x = 2y\) into the hypotenuse equation

Substitute \(x = 2y\) into \(3y+1=x + 4\), we get \(3y+1=2y + 4\).

Step3: Solve for \(y\)

Subtract \(2y\) from both sides: \(3y-2y+1=2y-2y + 4\), so \(y+1=4\), then \(y = 3\).

Step4: Solve for \(x\)

Since \(x = 2y\), substitute \(y = 3\), then \(x=2\times3=6\).

Answer:

\(x = 6,y = 3\) (the last option)