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Look at the figure below:

Triangle ABC is a right triangle with an angle ABC equal to 90 degrees. The length of AC is 7 units and the length of AB is 5 units. D is a point above C. Triangle ADC is a right triangle with angle DAC equal to 90 degrees and DC parallel to AB.

What is the length, in units, of segment CD?

6
8.5
7
9.8

Respuesta :

Answer:

9.8

Step-by-step explanation:

I took the test, hope this helps!!!!

In triangle ADC length of segment CD = 9.8units .

What are similar triangles?

"Two triangles are said to be similar if the ratio of the their corresponding sides are in proportion or their corresponding angles are of equal measure."

Formula used

For two similar triangles ΔABC and ΔCAD

(AB /AC) =(AC / CD)

According to the question,

As per the diagram,

In ΔABC and ΔADC we have,

Given ,m ∠ABC = m ∠CAD         (each 90°)

           AB || CD , AC is the transversal.

Therefore,

           m ∠BAC = m ∠ACD           (Alternate angles between parallel lines)

By AA theorem of similar triangles,

ΔABC ~ ΔCAD

⇒ (AB /AC) = (AC / CD)             ( Condition for similar triangles)

Substitute the value as mentioned in diagram we get,

⇒( 5 / 7) = ( 7 / CD)

⇒ CD = ( 7× 7) / 5

⇒ CD = 9.8 units

Hence, Option(D) is the correct answer.

Learn more about similar triangle here

https://brainly.com/question/25882965

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