Answered

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Is there enough information shown on the triangles to say that the
two triangles are congruent?
(A) No. All three angles must be congruent to one another or the
two triangles aren't congruent.
(B) No. The corresponding angles aren't congruent, which means
that the triangles aren't congruent.
(C) Yes. All pairs of corresponding angles are congruent; therefore,
the two triangles are congruent.
(D) No. The corresponding pairs of sides must also be marked
congruent to determine that the triangles are congruent.

Is There Enough Information Shown On The Triangles To Say That The Two Triangles Are Congruent A No All Three Angles Must Be Congruent To One Another Or The Two class=

Sagot :

Answer: (D) No. The corresponding pairs of sides must also be marked  congruent to determine that the triangles are congruent.

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Explanation:

The arc markings tell us how the angles pair up, and which pairs are congruent. Eg: The double-arc angles are the same measure.

Despite knowing that all three pairs of angles are congruent, we don't have enough information to conclude the triangles are congruent overall. We can say they are similar triangles (due to the AA similarity theorem), but we can't say they are congruent or not. We would need to know if at least one pair of sides were congruent, so that we could prove the triangles congruent.

The list of congruent theorems is

  • SSS
  • ASA
  • AAS (or SAA)
  • SAS
  • HL
  • LL

Much of these involve an "S", to indicate "side" (more specifically "pair of sides). Both HL and LL involve sides as well. They are special theorems dealing with right triangles only.

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So in short, we don't have enough info. We would have to know information about the sides. This is why choice D is the answer.

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