Question

Geometry homework help

Answer 1

Explanation:

(A) It is given that triangle JKL and JMN are similar, the using the basic proportionality theorem, we get

`(JK)/(JM)=(JL)/(JN)`

⇒
`(4)/(4+y-2)=(8)/(20)`

⇒
`(4)/(y+2)=(8)/(20)`

⇒
`10=2+y`

⇒
`y=8`

Since, triangle JKL and JMN are similar, we get

`(KL)/(KM)=(JL)/(JN)`

⇒
`(x)/(30)=(8)/(20)`

⇒
`x=\frac{8{*}30}{20}`

⇒
`x=12`

(B) a. AB is parallel to DE as when she heads from point A to point D, she takes a turn in right angle way and then again she heads to point E by taking a right angle turn, which shows that she is following the same path, thus AB is parallel to DE.

b. Since, AB is parallel to DE, therefore, ∠CAB=∠CED (Alternate angles) and ∠ACB=∠ECD (Vertically opposite angles).

c. Since, ΔABC is similar to ΔCDE, using basic proportionality theorem,

`(AB)/(CD)=(CB)/(DE)`

⇒
`(4)/(6)=(3)/(x)`

⇒
`x=\frac{3{*}6}{4}`

⇒
`x=(9)/(2)m`

Thus, DE=
`(9)/(2)m`