Are the triangles shown in the diagram congruent? If so, according to which congruence theorem?
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Are the triangles shown in the diagram congruent? If so, according to which congruence theorem?
To answer the question, we need to know the fourth congruence theorem: S.A.S.
The theorem states that triangles are congruent when they have an equal pair of sides and an equal angle.
However, there is one condition: the angle must be opposite the longer side of the triangle.
We start with the sides:
DF = CB = 16
GD = AC = 9
Now, we look at the angles:
A = G = 120
We know that an angle of 120 is an obtuse angle and this type of angle is always opposite the larger side of the triangle.
Therefore, we can argue that the triangles are congruent according to the S.A.S. theorem.
Congruent according to S.A.S.
Determine whether the triangles DCE and ABE congruent?
If so, according to which congruence theorem?
In any triangle, the largest angle is always opposite the longest side. Since 120° is obtuse (greater than 90°), it must be the largest angle, so it's opposite the side of length 16.
We have two sides (16 and 9) with the angle between them. In ASA, we'd need two angles with the side between them. The key is identifying what's between what!
Look for matching measurements and similar positions. Both triangles have sides of 16 and 9, with a 120° angle. The side lengths and angle positions help you match corresponding parts.
No, because we're only given two sides and one angle. For SSS congruence, we'd need all three sides of both triangles to be equal.
That would be impossible! In geometry, the largest angle must be opposite the longest side. A 120° angle (the largest) cannot be opposite a 9-unit side when there's a 16-unit side in the same triangle.
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