Which of the following statements is needed in order to prove these triangles are congruent using SSS?
BCA= EFD
CA ED
DE ~ BC
AB- DE
The missing statement needed in order to prove these triangles are congruent using SSS is:
AB = EF
Choose from the four given
Apologies for the incorrect response. The correct missing statement needed in order to prove these triangles are congruent using SSS is:
AB = DE
To prove that two triangles are congruent using the Side-Side-Side (SSS) congruence criterion, we need to show that all three pairs of corresponding sides are congruent.
In this case, the given statements are:
1. BCA = EFD
2. CA = ED
3. DE ~ BC
4. AB - DE
We need to determine which of these statements is necessary to prove the congruence of the triangles.
First, let's understand the SSS congruence criterion. It states that if the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent.
Now let's analyze the given statements one by one:
1. BCA = EFD: This statement compares the angles BCA and EFD. However, the congruence of angles is not a criterion for proving SSS congruence. Therefore, this statement is not needed to prove SSS congruence.
2. CA = ED: This statement compares the sides CA and ED. Since it states that these two sides are congruent, it provides the necessary information for one pair of corresponding sides to be equal. This statement is important for proving SSS congruence.
3. DE ~ BC: This statement states that side DE is proportional to side BC. Proportional sides do not guarantee congruence, so this statement is not needed for proving SSS congruence.
4. AB - DE: This statement is not clear, as it gives a subtraction expression rather than a direct comparison of sides. Without further information, we cannot determine whether this statement is relevant for proving SSS congruence.
In conclusion, the statement "CA = ED" is needed to prove the congruence of the triangles using SSS.