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densk [106]
3 years ago
6

What is the length of DE

Mathematics
1 answer:
HACTEHA [7]3 years ago
8 0

Answer:

DE = 20units

Step-by-step explanation:

In Δ ABC,

angle A is congruent to angle B.... (given)

therefore, ΔABC is an isoceles triangle.

therefore, CA = CB..... (side opposite to congruent angles are congruent in an isoceles triangle)

therefore, CB = 4 units

In ΔCDE,

angle D is congruent to angle E.... (given)

therefore, ΔCDE is an isoceles triangle.

therefore, CD = CE

therefore, CD = 8 units

ΔCDE ~ ΔCBA

therefore,

\frac{cd}{cb}  =  \frac{ce}{ca} =  \frac{de}{ab}   \\ therefore \:  \frac{8}{4}  =  \frac{8}{4}  =  \frac{de}{10 }  \\ therefore \\  \frac{2}{1 }  =  \frac{de}{10 }  \\ de \:  = 2 \times 10 = 20units

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