Question

I can determine the conditions for a unique triangle more than one triangle or no triangle 18. The cards below contain clues determine whether the conditions will result in one unique triangle more than one triangle or no triangle Justify your solution with a sketch and description below

Answer 1

Explanations:

A triangle is said to be unique if the sum of the two shorter sides is greater than the third side or if the sum of its two angles is less than 180 degrees.

On the other hand, if the sum of the two shorter sides is less than the third side, then no triangle is formed.

For us to have more than one triangle, the sum of the sides of the triangle must sum up to 180 degrees.

For the triangle ABC

The two shorter sides are 6.3cm and 4.2cm

Sum of two shorter sides = 6.3cm + 4.2cm = 10.5cm

Since AB + BC > CA,hence triangle ABC is a unique triangle

For the triangle DEF

DE = 2cm

EF = 3cm

FD = 5cm

Since the sum of DE and EF is not greater than FD, hence the triangle is not unique. We can see that the sum of DE and EF is equal to FD, hence the length of DE and EF cannot meet. The triangle formed by △DEF is a no triangle.

For the triangle GHI

Since the sum of any of its two angles is less than 180 degrees then triangle GHI is a unique triangle.

ALso