Find the side lengths of ∆ABC. What kind of triangle is it: scalene, isosceles, or equilateral?
Hint
The points are there. The distance formula is known. The rest is up to you.
Answer
∆ABC has side lengths of about 13.9, 12.5, and 9.2. The triangle is definitely scalene.
Example 2
If a triangle was formed from the midpoints of each of the segments, what would be the side lengths and type of the new triangle?
Hint
Remember that the midpoint formula is M = .
Answer
The lengths of the new triangle are roughly 4.6, 6.3, and 7.0. This triangle would also be scalene.
Example 3
∆DEF is an isosceles triangle on the coordinate plane. If D has the coordinates (-a, 0), what coordinates does E have?
Hint
It's on the y–axis. What does that tell you about the x coordinate?
Answer
E has the coordinates (0, b) because there are no specifications for the y coordinate of point E.
Example 4
What coordinates does F have?
Hint
The triangle is isosceles, remember?
Answer
F has the coordinates (a, 0) because it must be the same horizontal distance away from the origin as D.
Example 5
If ∆DEF was given the coordinates D (-3, 0), E (0, ), and F (3, 0), what kind of triangle would ∆DEF be?
Hint
Calculate the distances.
Answer
∆DEF would be not only isosceles, but also equilateral.
Example 6
∆JKL has coordinates at J (0, 0), K (1, 3), and L (3, 1), while ∆MNO has coordinates at M (1, -3), N (2, -6), and O (-1, -5). Are the two triangles congruent?
Hint
Calculate the distances of all the sides. That'll put SSS to use.
.
), and F (3, 0), what kind of triangle would ∆DEF be?