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.