Question

1 multiple choice 2 points the figure implies that ( ef + eg ) fg. 2 multiple choice 2 points find the length of ( overline{yz} ) if ( xz ) is 10, ( wz ) is 14, and ( wy ) is 11.

Explanation:

Problem 1

Step1: Apply the triangle inequality theorem

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. For \(\triangle EFG\), we have \(EF + EG>FG\)

Step1: Use the segment - addition postulate

We know that \(WZ = WY+YZ\) (by the segment - addition postulate: if \(Y\) lies on \(\overline{WZ}\), then \(WZ=WY + YZ\)). We are given that \(WZ = 14\) and \(WY=11\)

Step2: Solve for \(YZ\)

Substitute the given values into the equation \(WZ = WY+YZ\). So, \(YZ=WZ - WY\)

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Answer:

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Problem 2