If GH ≅ GJ, HI = 8t, and IJ = t + 63, what is the value of t?

Since GH ≅ GJ, we know that HI = IJ. So, we have 8t = t + 63.

Subtracting t from both sides, we get 7t = 63.
Dividing both sides by 7, we find that t = 9. Answer: \boxed{9}.

To find the value of t, we need to use the given information that GH ≅ GJ, HI = 8t, and IJ = t + 63.

Since GH ≅ GJ, we can conclude that HI = HJ.

Therefore, HI = HJ = 8t.

Given that IJ = t + 63, we can substitute the value of HJ (which is also HI) into the equation:

8t = t + 63.

To solve for t, we can start by subtracting t from both sides of the equation:

8t - t = t + 63 - t.

This simplifies to:

7t = 63.

Finally, to isolate t, we divide both sides of the equation by 7:

7t / 7 = 63 / 7.

This gives us:

t = 9.

Therefore, the value of t is 9.

To find the value of t, we need to use the given information and apply the concept of congruent triangles.

Given: GH ≅ GJ, HI = 8t, and IJ = t + 63.

Since GH ≅ GJ, we can say that the segments HI and IJ are also congruent. This means that HI = IJ.

Therefore, we can set up the equation HI = IJ as follows:

8t = t + 63

To solve this equation, we can simplify it by combining like terms:

8t - t = 63

Simplifying further:

7t = 63

To isolate t, divide both sides of the equation by 7:

t = 63/7

Simplifying the right side:

t = 9

Therefore, the value of t is 9.