Determine whether the ratios of the lengths of the trapezoids' corresponding sides are equal.
Yes, see solution.
Practice makes perfect
Let's start by recalling that two figures are said to be similar if they have the same shape. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. Hence, to determine whether the trapezoids are similar, let's find the lengths of their sides. We will use the Distance Formula.
d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Since the trapezoids are said to be equilateral, their two legs have the same length. We only need to find the lengths of the bases and the length of one leg. Let's start with ABCD. Using the given coordinates, we can graph the trapezoid.
As we can see, the bases of the trapezoid are 4 and 16 units long. Let's substitute (x_1,y_1) with A(0,0) and (x_2,y_2) with B(6,8) into the Distance Formula and calculate AB.
Similarly, we can find the length of the bases and one leg of AFGH. We will start with graphing it on a coordinate plane.
Again, using the diagram we can see that the bases of the trapezoid are 2 and 8 units long. To find the length of the legs, we will substitute (x_1,y_1) with A(0,0) and (x_2,y_2) with F(3,4) into the Distance Formula.
Now that we know the lengths of all the sides of both trapezoids, let's analyze the ratio of the corresponding sides.
All we need to do is find the ratio of the corresponding sides' length.
AH/AD? =AF/AB? =FG/BC
[0.6em]
8/16 ? = 5/10 ? = 2/4 [0.6em]
1/2 = 1/2 = 1/2
As we can see the ratios are equal, which allows us to conclude that ABCD and AFGH are similar trapezoids.
