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  • 13-02-2021
  • Mathematics
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Let AB // ED , AB = 10 units, AC = 12 units, and DE = 5 units. What is the length of AD?​

Let AB ED AB 10 units AC 12 units and DE 5 units What is the length of AD class=

Respuesta :

eudora eudora
  • 18-02-2021

Answer:

length of CD = 18 units.

Step-by-step explanation:

In ΔABC and ΔCED,

AB║DE and AD is a transversal line,

m∠ABC = m∠CED [Alternate interior angles]

m∠ACB = m∠DCE [Vertically opposite angles]

ΔABC ~ ΔCED [By AA property of similarity]

Therefore, by the property of similar triangles, corresponding sides will be proportional.

[tex]\frac{AB}{DE}= \frac{AC}{DC}[/tex]

[tex]\frac{10}{5}=\frac{12}{CD}[/tex]

CD = 6

Since, AD = AC + CD

AD = 12 + 6

     = 18 units

Therefore, length of CD = 18 units.

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