Chapter 10.2, Problem 14WE

(a)

To determine

To Draw: an acute triangle and construct perpendicular bisector of each side.

Answer to Problem 14WE

  $5\sqrt{5}$

Explanation of Solution

Given:

An acute triangle.

Calculation:

An acute is in which all interior angles are less than ${90}^{\circ }$ is drawn below.

  

First, draw perpendicular bisector of side AB using following steps.

1. Using C as center, draw two arcs of equal radii that intersect AB at X and Y.
2. Using X and Y as centers and a suitable radius, draw arcs that intersect at point Z.
3. Join CZ, it is a perpendicular bisector of side AB as shown below.

Similarly, perpendicular bisector side BC and AC are drawn as shown below.

  

(b)

To determine

To Find: whether the perpendicular bisector to all side in an acute triangle intersect at a point or not.

Answer to Problem 14WE

Explanation of Solution

Given:

An acute triangle with perpendicular bisectors.

Calculation:

Perpendicular bisectors are drawn is shown below.

  

Yes, they do intersect at a point.

(c)

To determine

To Draw: an acute triangle and construct perpendicular bisector of each side.

Answer to Problem 14WE

  $5\sqrt{5}$

Explanation of Solution

Given:

An obtuse triangle.

Calculation:

An obtuse is in which one angles is greater than ${90}^{\circ }$ is drawn below.

  

First, draw perpendicular bisector of side AB using following steps.

1. Using C as center, draw two arcs of equal radii that intersect AB at X and Y.
2. Using X and Y as centers and a suitable radius , draw arcs that intersect at point Z.
3. Join CZ, it is a perpendicular bisector of side AB as shown below.

Similarly perpendicular bisector side BC and AC are drawn as shown below.