HELP!! MEDAL + FAN
Use the figure below to answer the question that follows:
What must be given to prove that ΔBJI ~ ΔCJG?
A. segment BH is congruent to segment CH and segment BG is congruent to segment CI
B. ∠BIJ ≅ ∠CGJ and ∠JBI ≅ ∠JIB
C. segment BI is congruent to segment CG and
D. segment JI is congruent to segment JG
∠BIJ ≅ ∠CGJ and ∠BJI ≅ ∠CJG

- anonymous

- jamiebookeater

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- anonymous

##### 1 Attachment

- anonymous

- mathstudent55

Which methods of proving triangles similar do you know?

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## More answers

- anonymous

SAS, SA, SSS

- anonymous

angle side*

- mathstudent55

I know:
AA
SAS Similarity
SSS Similarity

- anonymous

aa yes sorry i forgot that one.

- mathstudent55

In your given problem, do the triangles have any pair of sides or angles that is congruent?

- anonymous

yes

- mathstudent55

|dw:1441305297304:dw|

- mathstudent55

I drew the figure twice above because the triangles we are trying to prove similar overlap, so I think it's easier to separate the figures.

- mathstudent55

|dw:1441305484271:dw|

- mathstudent55

This new figure shows the triangles we want to prove similar.
Which pair of angles or sides do they have in common that we know are congruent?

- anonymous

BF and EC?

- mathstudent55

No.
We are not told anything bout BF and EC, and also, BF and EC are not sides of our two triangles.

- mathstudent55

|dw:1441305708106:dw|

- anonymous

BIJ

- mathstudent55

Look at the figure above.
Angle J is in common to both triangles, so we already have a pair of congruent corresponding angles.

- mathstudent55

- mathstudent55

Since we already have a pair of congruent angles, we will probably use AA or SAS Similarity, and not SSS Similarity.

- mathstudent55

To use AA, we need one more pair of corresponding angles that are congruent.
Let's look at the choices.

- anonymous

Wouldnt it be CJG? like it says there

- mathstudent55

In choice B, the congruent angles are not corresponding, so they don't help.

- mathstudent55

In choice A, the segments are not sides of our triangle, so choice A does not help.

- anonymous

So its between choice C and D.

- mathstudent55

In choice C, we have only one pair of corresponding sides congruent. That is not enough for SAS Similarity.

- mathstudent55

Let's try D.

- anonymous

D makes more sense to me

- mathstudent55

Yes, choice D shows a pair of congruent sides and two pairs of congruent angles.
Using the two pairs of congruent angles of choice D, we can prove the triangles similar by AA.

- anonymous

Thank you so much for helping!

- mathstudent55

You're welcome.

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