Question

Choose Yes or No to tell whether there is more than one way to draw a triangle with the given measures.

AB = 15 cm, BC = 20 cm, ∠B = 40° yes or no

AB = 15 cm, AC = 20 cm, ∠C = 40° yes or no

BC = 5 cm, AB = 10 cm, ∠A = 20° yes or no

AC = 5 cm, BC = 10 cm, AB = 14 cm yes or no

Answer 1

The answers are;

AB = 15 cm, BC = 20 cm, ∠B = 40° no

AB = 15 cm, AC = 20 cm, ∠C = 40° yes

BC = 5 cm, BA = 10 cm, ∠A = 40° yes

AC = 5 cm, BC = 10 cm, AB = 14 cm no

Explanation:

Here we have that

1. in ΔABC, sides AB = BA and BC as well as ∠B are known hence the two sides and the included angle of the triangle are known, hence the triangle is well defined, hence there is only one way to draw the triangle.

Therefore, the answer is No

2. in ΔABC, sides AB and AC as well as ∠C which is ∡ACB are known hence since the included angle ∠A of the triangle is not known, the triangle is not well defined, that is there are more than one way to draw the triangle.

Therefore, the answer is Yes

3. Similarly in ΔABC, sides BC and AB as well as ∠A which is ∡CAB are known hence since the required included angle ∠B of the triangle is not known, the triangle is not well defined, that is there are more than one way to draw the triangle.

Therefore, the answer is Yes

4. in ΔABC, sides AC and BC and AB are known, hence, ∠A, ∠B, and ∠C cn be found which indicates that the triangle is well defined, that is only one way to draw the triangle.

Therefore, the answer is No.