Chapter 7.3, Problem 19PSB

To determine

To calculate : The probability that the fourth statement can be proved

Answer to Problem 19PSB

The probability that the fourth statement can be proved is $\frac{3}{4}$

Explanation of Solution

Given information : The following statements are given

 a. $\angle C\cong \angle D$

 b. $\angle A\cong \angle F$

 c. $\overrightarrow{AC}\cong \overrightarrow{DF}$

 d. $\overrightarrow{AB}\cong \overrightarrow{EF}$

Formula used : Any triangle can be proved to be congruent if any two angles are given congruent, and at least one corresponding side is also congruent. Or, if two sides and the angle containing them are given congruent.

Calculation : we know that congruency can be proved if following options come up together.

1. a,c,b
2. a,c,d
3. c,b,d

thus, we calculate the probability as

  $P=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

Hence, we get

  $P=\frac{3}{C{}_3}=\frac{3}{4}$