Question

In ∆ABC shown below, line segment AB is congruent to line segment BC.
Given: line segment AB ≅ line segment BC

Prove: The base angles of an isosceles triangle are congruent.
The two-column proof with missing statement proves the base angles of an isosceles triangle are congruent. Which statement can be used to fill in the numbered blank space?

Answer 1

the options are:
a) ∆DAB ≅ ∆DBC
b) ∆ABD ≅ ∆ABC
c) ∆ABC ≅ ∆CBD
d) ∆ABD ≅ ∆CBD

Answer 2

@radar can u please help?

Answer 3

@mathstudent55 can u help?

Answer 4

@AkashdeepDeb can u help?

Answer 5

Draw a median from B to AC
The you'll have the given side as similar
And AD = CD
And also you have a common median for both divided triangles
So by SSS conguence theorem prove that the triangles are congruent and thus
by CPCT the base angles will be similar as they always are in an isoseles triangle! :)

Answer 6

but the options are:
the options are:
a) ∆DAB ≅ ∆DBC
b) ∆ABD ≅ ∆ABC
c) ∆ABC ≅ ∆CBD
d) ∆ABD ≅ ∆CBD
@AkashdeepDeb

Answer 7

And the 2 triangles are there in 2 of the options!
You have to see where the triangle ABD and CBD are and then prove their congruency! :)

Answer 8

so the answer is c??
@AkashdeepDeb

Answer 9

No c) doesn't have the required triangles!
So eliminate c) :)
Only A) and D) do!
But A) says ∆DAB ≅ ∆DBC
Which actually would mean that angle DAB = angle DBC [Which is wrong]
So which do you think would be the answer?

Answer 10

its D
@AkashdeepDeb

Answer 11

And you are Correct! :)

Answer 12

:) thanks

Answer 13

can u help me with one more question?
i'll post it in like a minute

Answer 14

Sure! :)

Answer 15

Kudos?

Answer 16

Doesn't a and d both describe the same triangles, but use a different order of vertices?