Geometry DS

[srcc25anu]

If angle ABC is 30 degrees, what is the area of triangle BCE?

1.Angle CDF is 120 degrees, lines L and M are parallel, and AC = 6, BC = 12, and EC = 2AC

2.Angle DCG is 60 degrees, angle CDG is 30 degrees, angle FDG = 90, and GC = 6, CD = 12 and EC = 12

OA: D

[neha24]

well it has to be D

[neha24]

st 1 can be thought as follows :in triangle EBC BC = EC =12 that means angles CEB = angle CBE thant concludes us to the fact that angle ABE is also 30 degree !!
so now u know the base as 12 and u know the ht and hence we can find the area of triangle EBC

st 2 is rather simple : all u r given is the area of a triangle b/w two two parallel lines with base as 6 and then u are asked the area of a triangle b/w those same parallel lines with base as 12 .honestly i didn't calculate st 2 .logically we know we can get the area !!

[Anju@Gurome]

Deleted.

[rseafsf]

can anyone elaborate on statement 1...how did you prove AB to be the height

@Neha ...how did u prove st 1 : "can be thought as follows :in triangle EBC BC = EC =12 that means angles CEB = angle CBE thant concludes us to the fact that angle ABE is also 30 degree !"

[neha24]

@Neha ...how did u prove st 1 : "can be thought as follows :in triangle EBC BC = EC =12 that means angles CEB = angle CBE thant concludes us to the fact that angle ABE is also 30 degree !"

AB bisects the side CE doesn't mean AB bisects the angle CBE.
This is a common misconception.

Refer to the diagram below.

i guess i did major part of calculation on my paper and didnt write it here !!
when i know that BC = EC =12 then in triangle ABC we have the following : (6/sin30) = (12/ sin BAC)
this gives us sin BAC = 1 ------> angle BAC =90 degree ----> angle ABE = 30

[Anju@Gurome]

i guess i did major part of calculation on my paper and didnt write it here !!
when i know that BC = EC =12 then in triangle ABC we have the following : (6/sin30) = (12/ sin BAC)
this gives us sin BAC = 1 ------> angle BAC =90 degree ----> angle ABE = 30

You skipped the most important part in your earlier post.
Sorry for assuming that you made a mistake.

[rseafsf]

thank u neha