Chapter 3.6, Problem 3PSA

a

To determine

The type of given triangle as per angles.

Answer to Problem 3PSA

The given triangle is a right-angle triangle

Explanation of Solution

Given information:

Given triangle has one of its angle equal to $90°$

Since

triangle’s one angle is equal to $90°$

Hence

Given triangle is a right angle triangle

b

To determine

The type of given triangle as per angles.

Answer to Problem 3PSA

Given triangle is an obtuse angle triangle

Explanation of Solution

Given information:

Given triangle has one angle as obtuse triangle

Since, given triangle has one angle as obtuse triangle

Hence given triangle is an obtuse angle triangle

c

To determine

The type of given triangle as per angles.

Answer to Problem 3PSA

Given triangle is an acute angle triangle

Explanation of Solution

Given information:

Given triangle has all of its angle as acute angle

Since, given triangle has all of its angle as acute angle

Hence, given triangle is an acute angle triangle

d

To determine

The type of given triangle as per angles.

Answer to Problem 3PSA

Given triangle is an acute angle triangle

Explanation of Solution

Given information:

Two angles in a triangle are $40°\&60°$ and one external angle is $100°$

Since, given triangle has all of its angle as acute angle

Hence, given triangle is an acute angle triangle

e

To determine

The type of given triangle as per angles.

Answer to Problem 3PSA

Given triangle is a right angle triangle

Explanation of Solution

Given information:

Triangle given has one side perpendicular on other side, i.e., $\overline{\text{GH}}\perp \overline{\text{HJ}}$

Since given triangle GHJ has one side perpendicular on other side, i.e., $\overline{\text{GH}}\perp \overline{\text{HJ}}$

Hence given triangle GHJ is right angle triangle

f

To determine

The type of given triangle as per angles.

Answer to Problem 3PSA

Given triangle KMO is an equilateral triangle

Explanation of Solution

Given information:

Given triangle KMO has angles as

  $\begin{array}{l}\frac{1}{2}\left(\text{m}\angle \text{K}\right)=30\\ \frac{1}{3}\left(\text{m}\angle \text{M}\right)=20\\ \frac{1}{4}\left(\text{m}\angle \text{O}\right)=15\end{array}$

Since, angles of the given triangle KMO are given by

  $\begin{array}{l}\frac{1}{2}\left(\text{m}\angle \text{K}\right)=30\Rightarrow \left(\text{m}\angle \text{K}\right)=60°\\ \frac{1}{3}\left(\text{m}\angle \text{M}\right)=20\Rightarrow \left(\text{m}\angle \text{M}\right)=60°\\ \frac{1}{4}\left(\text{m}\angle \text{O}\right)=15\Rightarrow \left(\text{m}\angle \text{O}\right)=60°\end{array}$

and it is observed that all angles have equal measures and equal to $60°$

Hence, given triangle is an equilateral triangle