lucianojoseph594
Answered

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Consider the figure below. Which statement is most correct about the triangles?
a). ΔTRP~ΔTSG by SAS~

b). ΔTRP~ΔTSG by SSS~

c). ΔTRP~ΔTSG by AA~

d.) Similarity cannot be concluded with the information given

Consider The Figure Below Which Statement Is Most Correct About The Triangles A ΔTRPΔTSG By SAS B ΔTRPΔTSG By SSS C ΔTRPΔTSG By AA D Similarity Cannot Be Conclu class=

Sagot :

Answer: Choice C

ΔTRP~ΔTSG by AA~

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Further Explanation:

Triangles TRP and TSG share an overlapping angle at point T. This is one pair of congruent angles.

Due to the parallel lines (PR and GS), we can get two more pairs of congruent angles:

  • angle TSG = angle TRP
  • angle TGS = angle TPR

These congruences are valid because of the corresponding angle theorem.

You could use all three, but at minimum, you only need 2 pairs of congruent angles. Once we have two pairs of congruent angles, we can use the AA (angle angle) similarity theorem. Your teacher has abbreviated this as AA~

We cannot use SAS and SSS because we don't have any information about the sides.

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