Question

Use the diagram to find the value of "y" so that △AOC ≅ △ZFD by HL.

Answer 1

`y = 23`.

Explanation:

Two right triangles are congruent by the
`\texttt{HL}` postulate if and only if:

• One leg of the first right triangle (one of the two sides adjacent to the right angle) is equal in length to a leg of the other triangle.
• The hypotenuses of the two right triangles (opposite to the right angle) are equal in length.

In this example, the hypotenuses of the two right triangle are
`\textsf{CO}` and
`\textsf{FD}`, respectively.

For these two right triangles to be congruent by
`\texttt{HL}`, these two lengths should be equal to one another. Equate these two lengths and solve for
`y`:

`\textsf{CO} = \textsf{FD}`.

`73 = (3\, y + 4)`.

`y =23`.