What data must be added so that the triangles are congruent?
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What data must be added so that the triangles are congruent?
Let's consider that:
DF = AC = 8
DE = AB = 5
8 is greater than 5, therefore the angle DEF is opposite the larger side and is equal to 65 degrees.
That is, the figure we are missing is the angle of the second triangle.
We will examine which angle is opposite the large side AC.
ABC is the angle opposite the larger side AC so it must be equal to 65 degrees.
Angle ABC equals 65.
Look at the triangles in the diagram.
Which of the statements is true?
Angle ACB is opposite side AB (length 5), not the longest side AC (length 8). The largest angle must be opposite the longest side, so angle ABC = 65°.
Match the given measurements: DE = AB = 5, DF = AC = 8, and EF = BC. The angle of 65° is opposite the longest side in both triangles.
Compare the numerical values: 8 > 5, so AC (length 8) is the longest side in triangle ABC. The angle opposite AC is angle ABC.
SSA means Side-Side-Angle. We have two corresponding sides (5 and 8) and the angle opposite one of them (65°). This can determine congruence when the angle is opposite the longer side.
No! Since we already have two sides of each triangle, we need the angle between them or the angle opposite the longest side for congruence. Only angle ABC = 65° works here.
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