Chapter 10.2, Problem 15WE

a.

To determine

the figure of the acute triangle and constructing the three altitudes.

Explanation of Solution

Given:

Acute triangle

Acute triangle is a triangle having all the angles less than $90°$ .

Drawing an acute triangle,

  

Now measuring the angles,

  

And the sum of the angle is $180°$ .

Now forming the altitude,

  

As the angle lie inside the acute triangle they must have same meeting point of altitude as it is shown above.

Conclusion:

Therefore, the above figure is the figure of the acute triangle and constructing the three altitudes.

b.

To determine

whether the altitude meet at the same point or not.

Explanation of Solution

Given:

Acute triangle

Acute triangle is a triangle having all the angles less than $90°$ .

Drawing an acute triangle,

  

Now measuring the angles,

  

And the sum of the angle is $180°$ .

Now forming the altitude,

  

As the angle lie inside the acute triangle they must have same meeting point of altitude as it is shown above.

Conclusion:

Therefore, the above figure is the figure of the acute triangle and all the three altitude meet at a single point.

c.

To determine

the figure of the obtuse triangle and constructing the three altitude and whether the altitude meet at the same point or not.

Explanation of Solution

Given:

Obtuse triangle

Obtuse triangle is a triangle having one angle more than $90°$ rest all the angles is acute.

Drawing an Obtuse triangle,

  

Now measuring the angles,

  

And the sum of the angle is $180°$ .

Now forming the altitude,

  

For an obtuse triangle, the altitudes from the two acute angles intersect only the extensions of the opposite sides.

Conclusion:

Therefore, the above figure is the figure of the obtuse triangle and all the three altitude does not meet at a single point.