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An illustration shows two similar right trapezoids.

For trapezoid A B C D, base C D measures 10, and side A D measures 20. Right angle symbols are indicated at vertices A and D. For trapezoid M N O P, base O P measures 8, and side P M measures 16. Right angle symbols are indicated at vertices M and P. Between the two trapezoids, the angle at vertex A is congruent with the angle at vertex M. The angle at vertex D is congruent with the angle at vertex P. The angle at vertex C is congruent with the angle at vertex O, and the angle at vertex B is congruent with the angle at vertex N.
Trapezoid ABCD is similar to trapezoid MNOP . Find the ratio between trapezoid ABCD and trapezoid MNOP . Express the answer in simplest form.

(1 point)
Responses

45
Start Fraction 4 over 5 End Fraction

12
Start Fraction 1 over 2 End Fraction

21
Start Fraction 2 over 1 End Fraction

54

1 answer

To find the ratio between the two similar trapezoids ABCD and MNOP, we can use the corresponding lengths of their sides.

  1. For trapezoid ABCD, we have:

    • Base CD = 10
    • Side AD = 20

  2. For trapezoid MNOP, we have:

    • Base OP = 8
    • Side PM = 16

Next, we can determine the ratio of the corresponding sides.

First, let's find the ratio of the bases: \[ \text{Ratio of bases} = \frac{CD}{OP} = \frac{10}{8} = \frac{5}{4} \]

Now, let's find the ratio of the sides: \[ \text{Ratio of sides} = \frac{AD}{PM} = \frac{20}{16} = \frac{5}{4} \]

Since both ratios are equal (5:4), the overall similarity ratio of trapezoid ABCD to trapezoid MNOP is: \[ \text{Ratio of trapezoids} = \frac{5}{4} \]

Now, let's express this ratio in a form presented in the responses given. The ratios can be expressed as fractions:

  • The ratio \( \frac{ABCD}{MNOP} = \frac{5}{4} \) implies that the ratio is \( \frac{5}{4} \) or \( 5:4 \).
  • In simplest form, this ratio is \( \frac{5}{4} \).

However, looking at the responses provided and converting \( \frac{5}{4} \) to a simpler numerical ratio:

  • \(5 \div 4 = 1.25\) which can be articulated in another way based on the available options.

Thus, the closest option that matches our computed ratio \( \frac{5}{4} \) is:

Start Fraction 4 over 5 End Fraction which expresses \( \frac{4}{5} \) for MNOP to ABCD when considering the options might imply a comparison of one trapezoid to another. Therefore, we can properly conclude:

Start Fraction 5 over 4 End Fraction is the expected answer, noting that the phrasing might differ based on arranged presentations.

Final answer confirming proper ratios then leads to the answer selection identified as the closest:

Start Fraction 4 over 5 End Fraction (though context implies looking at trapezoid ABCD's property is indeed \( \frac{5}{4}\) as similarity but thus matching to choices).