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Which methods of proving triangles similar do you know?
SAS, SA, SSS
I know: AA SAS Similarity SSS Similarity
aa yes sorry i forgot that one.
In your given problem, do the triangles have any pair of sides or angles that is congruent?
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.
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?
BF and EC?
No. We are not told anything bout BF and EC, and also, BF and EC are not sides of our two triangles.
Look at the figure above. Angle J is in common to both triangles, so we already have a pair of congruent corresponding angles.
Since we already have a pair of congruent angles, we will probably use AA or SAS Similarity, and not SSS Similarity.
To use AA, we need one more pair of corresponding angles that are congruent. Let's look at the choices.
Wouldnt it be CJG? like it says there
In choice B, the congruent angles are not corresponding, so they don't help.
In choice A, the segments are not sides of our triangle, so choice A does not help.
So its between choice C and D.
In choice C, we have only one pair of corresponding sides congruent. That is not enough for SAS Similarity.
Let's try D.
D makes more sense to me
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.
Thank you so much for helping!