Chapter 4.7, Problem 1WE

(a)

To determine

Draw a scalene triangle ABC. Draw the bisector of $\angle A$ , the altitude from A , and the median from A. All should be different.

Explanation of Solution

Calculation:

The diagram is :

  

M is the midpoint of BC. AM is the median.

AD is the altitude.

AE is the bisector of $\angle A$ .

(b)

To determine

Draw a isosceles triangle ABC with vertex angle A. Draw the bisector of $\angle A$ , the altitude from A , and the median from A. Find whether all the three are different.

Answer to Problem 1WE

The bisector of $\angle A$ , the altitude from A , and the median from A , all are congruent in isosceles triangle.

Explanation of Solution

Calculation:

The diagram is :

  

In an isosceles triangle , the angle bisector bisects the opposite side of the triangle at right angle. So, the bisector of $\angle A$ , the altitude from A , and the median from A , all are congruent in isosceles triangle.