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Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?

Answer :

Final answer:

To prove triangle similarity by the SAS similarity theorem, identified statements should show proportional corresponding sides and congruent included angles between those sides. These statements usually involve the ratios of side lengths and the measures of angles.

Explanation:

To prove that triangles are similar by the SAS (Side-Angle-Side) similarity theorem, we must find statements that show two pairs of corresponding sides are proportional and the included angle between those sides is congruent in both triangles. When looking at a diagram or problem involving triangles, it's important to identify these particular pairs of sides and the angle. For instance, if we have triangles ABC and DEF where side AB is proportional to side DE, side AC is proportional to side DF, and angle A is congruent to angle D, then we can say that the triangles ABC and DEF are similar by the SAS similarity theorem.

The statements that usually lead to this conclusion involve equal ratios of side lengths and equal measures of the included angles. For example:

  • The ratio of side AB to side DE equals the ratio of side AC to side DF (proportionality of sides).
  • Angle A is congruent to angle D (equality of the included angle).

These statements are what we would look for in a geometry problem to apply the SAS similarity theorem.

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