Question

Identify the similar triangles in the figure then find the value of X.

A. Write the similarity statement in the form of triangle~triangle.
B. What is the value of X.

Answer 1

x = 8

Explanation:

∠ B ≅ ∠ D

∠ A ≅ ∠ C

Then

Δ BAD ≅ Δ DCE ( AA postulate )

Then the ratios of corresponding sides are equal, that is

`(BA)/(DC)` =
`(BD)/(DE)` , substitute values

`(x)/(4)` =
`(12)/(6)` = 2 ( multiply both sides by 4 to clear the fraction )

x = 8