Chapter 4.1, Problem 22WE

a.

To determine

To draw each triangle accurately and tell whether it will be congruent to any of my class mates.

Explanation of Solution

Given:

In $△RST$ , $RS=4cm$ , $m\angle S=45$ and $ST=6cm$

Calculation:

The following is the required triangle-

  

The given triangle will be congruent to that of my classmates because the two sides and an angle are specified.

b.

To determine

To draw each triangle accurately and tell whether it will be congruent to any of my class mates.

Explanation of Solution

Given:

In $△UVW$ , $m\angle U=30$ , $UV=5\text{ cm}$ and $m\angle V=100$

Calculation:

The following is the required triangle-

  

The given triangle will be congruent to that of my classmates because the two angles and one side are specified.

c.

To determine

To draw each triangle accurately and tell whether it will be congruent to any of my class mates.

Explanation of Solution

Given:

In $△DEF$ , $m\angle D=30$ , $m\angle E=68$ and $m\angle F=82$

Calculation:

The given triangle will not be congruent to that of my classmates because they can choose different measurement of sides.

d.

To determine

To draw each triangle accurately and tell whether it will be congruent to any of my class mates.

Explanation of Solution

Given:

In $△XYZ$ , $XY=3cm$ , $YZ=5\text{ cm}$ and $XZ=6cm$

Calculation:

The following is the required triangle-

  

The given triangle will be congruent to that of my classmates because of the SSS postulate.