Geometric Reasoning: Find Angle ABC in Rhombus ABDF

  • Thread starter Thread starter Natasha1
  • Start date Start date
  • Tags Tags
    Geometric
Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
24 replies · 3K views
Natasha1
Messages
494
Reaction score
9

Homework Statement


As shown in the diagram (attached), ABDF is a rhombus, ACE is an equilateral triangle, and AB  AC . Find ABC through geometric reasoning (a scale diagram will gain no credit).

2. See drawing (picture attached)
Screen Shot 2016-03-24 at 21.36.19.png

The Attempt at a Solution


If I make angle ABC = x then BCA is also = x (as triangle ABC is isosceles) so I got x + x + 180 - 2x = 180

angles ACE = CEA = EAC = 60 degrees (Equilateral triangle)

Must I use alternate angles to help me solve this problem...
 
on Phys.org
if BCA = x then CAF = x (alternate angles)

CAE = 60 but what is EAF = ?
 
how does that help me?
 
So we have ABC = BDF = DFA = x
 
So ABC = DFA = x

in each triangle we get x + x + 180 - 2x = 180 (but then this is obvious)
 
In quadrilateral CEFA we have 60+x+x+180-2x+60+60=360 but then 360 = 360 leads nowhere
 
all 4 sides are equal in a rhombus
 
Natasha1 said:
i give up
As you said, all four sides are equal in a rhombus. That is not true of a parallelogram. In a parallelogram, which sides must be equal? Which sides need not be equal? Answer in terms of 'adjacent' and 'opposite'.
 
As you said, all four sides are equal in a rhombus. That is not true of a parallelogram. In a parallelogram, which sides must be equal? Which sides need not be equal? Answer in terms of 'adjacent' and 'opposite'.

In the rhombus ABDF, AB = BD = DF = FA
In a parallelogram opposite = equal, adjacent = not equal
 
is x = 30 degrees? (a guess)
 
How can knowing that triangles ABC and AFE are isosceles and similar help me in finding angle ABC?
 
Natasha1 said:
As you said, all four sides are equal in a rhombus. That is not true of a parallelogram. In a parallelogram, which sides must be equal? Which sides need not be equal? Answer in terms of 'adjacent' and 'opposite'.

In the rhombus ABDF, AB = BD = DF = FA
In a parallelogram opposite = equal, adjacent = not equal
Right, so pick some pair of adjacent sides.. AB and BD say. You know these are equal. What isosceles triangle does that give you?
 
similar isosceles triangles
 
Natasha1 said:
similar isosceles triangles
I mean with reference to the points in the diagram. Choose two adjacent sides of the rhombus and say which you have chosen. You know they are equal length, so they form two sides of an isosceles triangle. Which triangle? What angles are therefore equal?
 

Similar threads

Find $\angle BPC$ in Triangle ABC with $\angle ACB=\angle ABC=80^\circ$
  • anemone
  • · Replies 14 ·
  • General Math
Replies
14
Views
4K