Are the triangles in the image congruent?
If so, according to which theorem?
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Are the triangles in the image congruent?
If so, according to which theorem?
Although the lengths of the sides are equal in both triangles, we observe that in the right triangle the angle is adjacent to the side whose length is 7, while in the triangle on the left side the angle is adjacent to the side whose length is 5.
Since it's not the same angle, the angles between the triangles do not match and therefore the triangles are not congruent.
No.
Determine whether the triangles DCE and ABE congruent?
If so, according to which congruence theorem?
The position of the angle matters! In one triangle, the 39° angle is between sides 5 and 7, but in the other triangle, the 39° angle is between different sides. For SAS congruence, the angle must be between the same pair of corresponding sides.
SAS (Side-Angle-Side) is very specific: you need two sides and the included angle between them. Just having equal parts isn't enough - the angle must be sandwiched between the two equal sides in both triangles.
Look at the vertex where the angle is located. The two sides that meet at that vertex are the sides that form the angle. In this problem, trace from the 39° angle to see which two sides it connects.
Let's check! We don't have all three sides (SSS), we don't have two angles and a side (ASA or AAS), so no other congruence theorem applies here. The angle positioning prevents any congruence.
To be congruent by SAS, the 39° angle would need to be between the same pair of sides in both triangles. For example, both angles should be between the sides of length 5 and 7.
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