Geometry Problem HELPPPPPPPPPP urgentttt NEWWWWWW

[arifaisal]

Q1-In ABC, angle AFB=angle AEC=90. If BF=CE, which of the following must be true?

A)AB=AC
B)AE=CE
C)BF=AF
D)AB=BC
E)none

Q2-In the figure, AD||BC. AB=5 cm and AD=7 cm. If angle BCD=1/2 angle BAD, what is the length of BC in cm?
A)10
B)12
C)17
D)19
E) cannot be determined

Q3-In the figure below, D is the midpoint of AB and E is the midpoint of AC. What is the relation between the area of BFC and the area of ADFE?

A)Area BFC> area ADFE
B)Area BFC= area ADFE
C)Area BFC< area ADFE
D)area ADFE= 1.5 times Area BFC
E) either A or C

please give full explanation and check the figure for reference

[shankar.ashwin]

Pls stick to one question per post.

Question 2:

The given figure will be a trapezoid, let the angles be A,B,C and

A + B = 180 and C + D = 180

A + B = 180 and 2A + D = 180. Given AB =5 and AD = 7, we cannot determine the finite angles for the figure IMO. BC would vary depending on angles C and A. Cannot be determined IMO. Not very sure though.

[Neo Anderson]

Question 1

Area of the trianle here can be calculated as:
1/2 * base* height = 1/2 *AB*CE = 1/2 *AC*BF
with given condition (BF=CE)
=> AB=AC
thus A

[Neo Anderson]

Question 2

extend the lines BA and CD to meet at o as shown above
now angle BCD = ADO = Q
as angle BAD = 2Q => angle DAO = 180 - 2Q => angle AOD = Q (sum of angles in trianle = 180
Thus now from two isoceles triangles AOD you have y=7 and from asoceles triangle you have x= 5+7=12
hence B

[Neo Anderson]

Question 3: IMO E; but for certain set of values (for length of the sides) the 2 area's can be equal also; :

[arifaisal]

Hey neo thanks alot...really helped me a lot...but q3 is not totally clear to me

[mankey]

For Ques3: IMO: B. Both areas will be equal. There is a property of triangles that three medians will divide triangle in 4 triangles of equal areas.

Thanks.

[saketk]

Answering Question 3 here --

This is the property of Median of a Triangle The three medians divide the triangle into 6 smaller triangles that all have the same area, even though they may have different shapes.


Please refer to the image I've attached.

The 3rd Median is dividing ADEF into 2 equal parts. i.e ADF and AEF. Also, it divided BFC into 2 equal parts.

That means ADEF combines will be EQUAL to BFC (two parts combined).

Answer should be Option B