anonymous
  • anonymous
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
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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mathstudent55
  • mathstudent55
Which methods of proving triangles similar do you know?

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anonymous
  • anonymous
SAS, SA, SSS
anonymous
  • anonymous
angle side*
mathstudent55
  • mathstudent55
I know: AA SAS Similarity SSS Similarity
anonymous
  • anonymous
aa yes sorry i forgot that one.
mathstudent55
  • mathstudent55
In your given problem, do the triangles have any pair of sides or angles that is congruent?
anonymous
  • anonymous
yes
mathstudent55
  • mathstudent55
|dw:1441305297304:dw|
mathstudent55
  • 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
  • mathstudent55
|dw:1441305484271:dw|
mathstudent55
  • 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
  • anonymous
BF and EC?
mathstudent55
  • mathstudent55
No. We are not told anything bout BF and EC, and also, BF and EC are not sides of our two triangles.
mathstudent55
  • mathstudent55
|dw:1441305708106:dw|
anonymous
  • anonymous
BIJ
mathstudent55
  • 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
mathstudent55
  • mathstudent55
Since we already have a pair of congruent angles, we will probably use AA or SAS Similarity, and not SSS Similarity.
mathstudent55
  • mathstudent55
To use AA, we need one more pair of corresponding angles that are congruent. Let's look at the choices.
anonymous
  • anonymous
Wouldnt it be CJG? like it says there
mathstudent55
  • mathstudent55
In choice B, the congruent angles are not corresponding, so they don't help.
mathstudent55
  • mathstudent55
In choice A, the segments are not sides of our triangle, so choice A does not help.
anonymous
  • anonymous
So its between choice C and D.
mathstudent55
  • mathstudent55
In choice C, we have only one pair of corresponding sides congruent. That is not enough for SAS Similarity.
mathstudent55
  • mathstudent55
Let's try D.
anonymous
  • anonymous
D makes more sense to me
mathstudent55
  • 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
  • anonymous
Thank you so much for helping!
mathstudent55
  • mathstudent55
You're welcome.

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