Question

What is ED ? Enter your answer in the box. units two segments A D and B C intersect at point E to form two triangles A B E and D C E. Side A B is parallel to side D C. A E is labeled 2 x plus 4. E D is labeled x plus 4. C D is 6 units. A B is 9 units.What is ED ?

Enter your answer in the box.



units


two segments A D and B C intersect at point E to form two triangles A B E and D C E. Side A B is parallel to side D C. A E is labeled 2 x plus 4. E D is labeled x plus 4. C D is 6 units. A B is 9 units.

Answer 1

E D is labeled x plus 4. ... two segments A D and B C intersect at point E to form two triangles A B E and D C E. Side A B ...

Answer 2

ED = 8 units.

Step-by-step explanation:

See the diagram attached.

If AB ║ DC, then, ∠ ABE = ∠ DCE {Alternate angles) and ∠ BAE = ∠ CDE {Alternate angles) and ∠ AEB = ∠ CED {Vertically opposite angles}.

Hence, Δ ABE will be similar to Δ DEC.

And hence, $\frac{AB}{CD} = \frac{AE}{DE}$

⇒ $\frac{9}{6} = \frac{2x + 4}{x + 4}$

⇒ 3(x + 4) = 2(2x + 4)

⇒ x = 4

Hence, ED = x + 4 = 4 + 4 = 8 units. (Answer)