Chapter 8, Problem 34RP

a.

To determine

Find the probability that his guess is correct.

Answer to Problem 34RP

  $\frac{1}{6}$

Explanation of Solution

Given information:

Filbert knows that $\Delta ABCand\Delta XYZ$ are similar, but he forget the correct correspondence of vertices should be. He guesses that $\Delta ABC\cong \Delta XYZ$ .

Calculation:

Here possible outcomes are, $XYZ,XZY,YXZ,YZX,ZXY,ZYX$

  $probability=\frac{1}{6}$

Hence, the probability that his guess is correct is $\frac{1}{6}$ .

b.

To determine

Find the probability for triangles are isosceles.

Answer to Problem 34RP

  $\frac{1}{3}$

Explanation of Solution

Given information:

Filbert knows that $\Delta ABCand\Delta XYZ$ are similar, but he forget the correct correspondence of vertices should be. He guesses that

  $\Delta ABC\cong \Delta XYZ$ .

Calculation:

Here possible outcomes are, $XYZ,XZY,YXZ,YZX,ZXY,ZYX$

Favorable outcome are two

  $probability=\frac{2}{6}=\frac{1}{3}$

Hence, the probability for triangles are isosceles $\frac{1}{3}$ .

c.

To determine

Find the probability for triangles are equilateral.

Answer to Problem 34RP

  $1$

Explanation of Solution

Given information:

Filbert knows that $\Delta ABCand\Delta XYZ$ are similar, but he forget the correct correspondence of vertices should be. He guesses that $\Delta ABC\cong \Delta XYZ$ .

Calculation:

Here possible outcomes are, $XYZ,XZY,YXZ,YZX,ZXY,ZYX$

Favorable outcome are six.

  $probability=\frac{6}{6}=1$

Hence, the probability for triangles are equilateral $1$ .