Chapter 4.5, Problem 13PPS

(a)

To determine

To explain:

The way to estimate the distance $FG$ across the lake by crew team

Answer to Problem 13PPS

The vertical angles theorem and angle side angle (ASA) theorems are used to estimate the distance $FG$ across the lake by crew team as $\overline{FG}\cong \overline{HJ}$ .

Explanation of Solution

Given information:

  

Since all right angles are congruent:

  $\angle HJK\cong \angle GFK$

Know that:

  $\overline{JK}\cong \overline{KF}$

Here, $\angle HKJ$ and $\angle FKG$ are vertical angles so, using the vertical angles theorem:

  $\angle HKJ\cong \angle FKG$

According to the angle side angle (ASA) congruence postulate gets that:

  $\Delta HJK\cong \Delta GFK$

The corresponding parts of congruent triangles are congruent, therefore:

  $\overline{FG}\cong \overline{HJ}$

(b)

To determine

To explain:

The lake long enough or not for the crew team to use as the location for their regatta

Answer to Problem 13PPS

No, the lake long is not enough to use as the location for their regatta for the crew team

Explanation of Solution

Given information:

  

Given that:

  $HJ=1350m$

From sub-part (a): $\overline{FG}\cong \overline{HJ}$ :

  $FG=HJ=1350m$

If the regatta is to be $1500m$ , the lake is not long enough, since $1350<1500$ .