Are the sides of the two new triangles proportional to the sides of the original triangle? If so, these new triangles are similar to the original one.
Type of Triangle:Right Explanation: See solution.
Practice makes perfect
Let's consider the Pythagorean triple 3, 4, and 5.
If we double the length of each side, we will get 6, 8, and 10.
Notice that the sides of the new triangle are proportional to the sides of the original triangle.
6/3 = 8/4 = 10/5 = 2
This means the two triangles are similar and so, the new triangle is a right triangle. Similarly, let's halve the length of each side of the original triangle. We get 1.5, 2, and 2.5.
Again, note that the sides of the new triangle are proportional to the sides of the original triangle.
1.5/3 = 2/4 = 2.5/5 = 1/2
In consequence, this new triangle is similar to the original one and so, it is also a right triangle.
