Chapter 2.3, Problem 16WE

a.

To determine

To find: congruent angles

Answer to Problem 16WE

  $\angle TSV,\angle RSV$ and $\angle SRU,\angle TRU$

Explanation of Solution

Given information: $\overrightarrow{SV}$ bisects $\angle RST$ and $\overrightarrow{RU}$ bisects $\angle SRT$

  

An angle bisector bisects the angle into two congruent angles.

As $\overrightarrow{SV}$ bisects $\angle RST$ ,

  $\angle TSV\cong \angle RSV$

As $\overrightarrow{RU}$ bisects $\angle SRT$ ,

  $\angle SRU\cong \angle TRU$

Therefore, pair of congruent angles are $\angle TSV,\angle RSV$ and $\angle SRU,\angle TRU$

b.

To determine

To find: additional information that enables to deduce that $m\angle VSU=m\angle URV$

Answer to Problem 16WE

Additional information required is $m\angle VSR=m\angle URS$

Explanation of Solution

Given information: $m\angle VSU=m\angle URV$

  

Use the pair of congruent triangles obtained in part a.

If two angles are congruent then their measures are also equal.

From part a., $\angle TSV\cong \angle RSV$

So,

  $m\angle TSV=m\angle RSV$ (i)

From part a., $\angle TRU\cong \angle SRU$

So,

  $m\angle TRU=m\angle SRU$ (ii)

Now assume that $m\angle VSR=m\angle URS$ (iii)

From (i), (ii) and (iii),

  $m\angle TSV=m\angle TRU$ (Things which are equal to the same thing are equal to each other)

That is

  $m\angle VSU=m\angle URV$

So, we get that $m\angle VSU=m\angle URV$ using the assumption that $m\angle VSU=m\angle URV$