A scalene triangle is a triangle that has no congruent sides..read on..?

Question

A scalene triangle is a triangle that has no congruent sides.

1. Use the information given in the triangle below to find AB, BC and AC.

2. Determine if the triangle is scalene or not based on the lengths of the three sides.

Show your work and support your conclusion

A(3,6)

B(6,3)

C(1,1)

Answer 1

First, draw the triangle on a graph. Next, what you want to do is find the lengths of the sides. For this, use the Pythagorean theorem (A squared + B squared = C squared). You will create separate right triangles making each line segment you have plotted the hypotenuse. So for AB, make your right triangle with the right angle at (6,6). Call that point whatever you want (I'll call it D). So we know that AD = 3 and BD = 3. 3 squared + 3 squared (9+9) = 18. So AB = √18.

Do the same for sides  AC and BC.

The work for AC: the right angle will be at (1,6). I'll call this point E. EC = 5 and AE = 2. Square those and add them. 25 + 4 = 29. AC = √29.

The work for BC: Make point F at (6,1). BF = 2 and CF = 5. square them and add them. 4 + 25 = 29. BC = √29. That happens to be the same as AC. So this is not a scalene triangle, but it is an isosceles triangle (one with 2 equal sides).

Answer 2

I will outline the solution for you. I will leave the actual calculations for you to do and for you to determine if the triangle defined by the three given points is scalene or not.

First step is to use the formula,

D = sqrt[(X1 - X2)^2 + (Y1 - Y2)^2]

to determine the distance between the points AB, AC and BC.

The second step is to compare the distances that have been calculated and from here you can determine what kind of triangle is defined by the three given points.

This is good mental exercise for you as well.