Look at the triangles in the diagram.
Which of the following statements is true?
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Look at the triangles in the diagram.
Which of the following statements is true?
This question actually has two steps:
In the first step, you must define if the triangles are congruent or not,
and then identify the correct answer among the options.
Let's look at the triangles: we have two equal sides and one angle,
But this is not a common angle, therefore, it cannot be proven according to the S.A.S theorem
Remember the fourth congruence theorem - S.A.A
If the two triangles are equal to each other in terms of the lengths of the two sides and the angle opposite to the side that is the largest, then the triangles are congruent.
But the angle we have is not opposite to the larger side, but to the smaller side,
Therefore, it is not possible to prove that the triangles are congruent and no theorem can be established.
It is not possible to calculate.
Determine whether the triangles DCE and ABE congruent?
If so, according to which congruence theorem?
S.S.A is not a valid congruence theorem! Two sides and a non-included angle can create different triangles. You need the angle to be between the two equal sides (S.A.S) or have all three sides equal (S.S.S).
Visual appearance can be deceiving! Triangles might look similar but not be congruent. You must use mathematical proof with S.A.S, A.S.A, or S.S.S theorems to establish congruence.
No! Without proving congruence first, you cannot assume corresponding angles are equal. The question asks what's true, and without congruence proof, none of the angle comparisons can be confirmed.
It means we cannot determine which statement is true because we lack sufficient information to prove the triangles congruent. When congruence can't be established, we can't make claims about corresponding parts.
The question focuses on congruence, not similarity. Even if triangles were similar, that wouldn't help us determine if corresponding sides are equal or make the given statements true.
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