Error 1: DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC, Error 2: The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1), Error 3:The third error is the value of x and we can find the correct value of x from the equation 14 / 7 = 16 / (x - 1) and the value of x is 9.
Given: The diagram is given and we need to find the errors and then fix them. Also ΔTSR ≈ ΔTCD
Let's solve the given question:
Given that ΔTSR ≈ ΔTCD
So we know by the properties of the similarity that if two triangles are similar then the ratio of their corresponding sides is equal.
So, ΔTSR ≈ ΔTCD
=> RT / TD = ST / TC
=> 14 / 7 = 16 / (x - 1)
In the question, we can observe that the given side ratio is DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC.
The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1).
The third error is the value of x.
We can find the correct value of x from the given equation:
14 / 7 = 16 / (x - 1)
=> 2 = 16 / (x - 1)
Multiplying both sides by (x - 1):
(x - 1) × 2 = 16 / (x - 1) × (x - 1)
=> 2(x - 1) = 16
Multiplying both sides by 1 / 2:
2(x - 1) × 1 / 2= 16 × 1 / 2
=> x - 1 = 8
Adding 1 on both sides:
x - 1 + 1 = 8 + 1
x = 9
Therefore x = 9.
Hence the errors are:
Error 1: DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC
Error 2: The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1).
Error 3:The third error is the value of x and we can find the correct value of x from the equation 14 / 7 = 16 / (x - 1) and the value of x is 9.
Know more about "similar triangles" here: brainly.com/question/14366937
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