Chapter 4.1, Problem 55PPS

(a)

To determine

To draw: Four isosceles triangles.

Explanation of Solution

Given information: The vertex opposite side $\overline{BC}$ is $\angle A$ .

  

Graph: The required triangles are given below,

• Acute triangle

  

• Right triangle

  

• Obtuse triangle

  

• Isosceles triangle

  

(b)

To determine

To measure: The sum of all the angle of each triangle.

Answer to Problem 55PPS

The required tabular are as follows.

  $\begin{array}{cccc}m\angle A& m\angle A& m\angle A& SumofangleMeasures\\ 55& 55& 70& 180\\ 68& 68& 44& 180\\ 45& 45& 90& 180\\ 30& 30& 120& 180\end{array}$

Explanation of Solution

Given information: The figures of triangles are as follows,

  

  

  

  

The angle of each triangle are added together and given into the tabular form.

  $\begin{array}{cccc}m\angle A& m\angle A& m\angle A& SumofangleMeasures\\ 55& 55& 70& 180\\ 68& 68& 44& 180\\ 45& 45& 90& 180\\ 30& 30& 120& 180\end{array}$

(c)

To determine

To measure: The sum of the all angles of an isosceles triangle.

Answer to Problem 55PPS

The angle of isosceles angle is $180°$ .

Explanation of Solution

Given information: The triangle is an isosceles triangle.

In an isosceles triangle the opposite angles of the congruent sides have the same measure. The sum of the all internal angles of an isosceles triangle is $180°$ .

(d)

To determine

To find: The expression for the measures of each other two angles in an isosceles triangle.

Answer to Problem 55PPS

The required expression for the measures of each angle is $x\&180°-2x$ .

Explanation of Solution

Given information: The triangle is an isosceles triangle.

In an isosceles triangle the opposite angles of the congruent sides have the same measure.

Let $x$ be the measures of one angle and as we now the sum of the all internal angles of an isosceles triangle is $180°$ .

Then, the other two angle of that isosceles triangle will be $180°-2x$ .