When a ratio has the form a:a, it means that the quantities compared are equal.
Isosceles trapezoid. See solution.
Practice makes perfect
We are asked to identify the described quadrilateral. Let d_1 and d_2 be the length of the diagonals of the quadrilateral. Since their ratio is 1:1, we can set the following equation.
d_1/d_2 = 1/1 ⇒
d_1 = d_2
Thus, the diagonals of the quadrilateral have the same length. Next, let's check the ratio of the lengths of consecutive sides.
3:4:3:5
Notice that the ratio of the first side to the third side is 3:3, which means that they have the same length. Also, by looking at the other ratios, we see that no other sides of the quadrilateral have the same length.
Characteristics of the Quadrilateral
Has only one pair of sides congruent
The congruent sides are opposite sides
Its diagonals are congruent
According to the two characteristics above, we can say that the quadrilateral we are dealing with is an isosceles trapezoid.
