What additional piece of information is needed in order to prove triangles EFG and HIJ are congruent by the SAS congruence theorem? F=H E=I G=I F=I

Answer 1

To prove triangles EFG and HIJ are congruent by the SAS (Side-Angle-Side) congruence theorem, you need to confirm that you have two sides of one triangle equal to two sides of the other triangle and the included angle between those two sides is equal.

From the information provided:

• F = H (one pair of corresponding vertices is equal)
• E = I (another pair of corresponding vertices is equal)
• G = I (there seems to be a mix-up with notation, but if G and I are supposed to be sides, that would need clarification).

For the SAS theorem specifically, you need:

1. Two sides of triangle EFG to be equal to two sides of triangle HIJ.
2. The angle between those two sides in one triangle to be equal to the angle between the corresponding two sides in the other triangle.

Since we have:

• F = H (this can be considered one side)
• E = I (this can be considered another side)

We still need the following:

• The length of EF must equal the length of HI (first side).
• The length of FG must equal the length of IJ (second side).
• The angle ∠EFG must equal ∠HIJ (the included angle).

In summary, to apply the SAS congruence theorem, we need one more piece of information: either the lengths of sides EF and HI, and side FG and IJ, along with the measure of the angle ∠EFG or ∠HIJ being equal. This will help establish congruence under the SAS criterion.

Answer 2

Choose an option that is provided.

Answer 3

It appears I have not been provided with specific options to choose from. Please provide the options you have, and I will help you determine which piece of information is necessary to prove triangles EFG and HIJ are congruent by the SAS congruence theorem.

Answer 4

Each of them are angles. Angle F = Angle H. Angle E = Angle I. Angle G = Angle I. Or Angle F = Angle I.

Answer 5

To prove triangles EFG and HIJ congruent using the SAS (Side-Angle-Side) congruence theorem, we need to establish that we have two sides in one triangle equal to two sides in the other triangle, and the angle included between those sides in one triangle is equal to the angle included between the corresponding sides in the other triangle.

Given the options:

1. Angle F = Angle H
2. Angle E = Angle I
3. Angle G = Angle I
4. Angle F = Angle I

Since we already have:

• F = H (which gives us one side)
• E = I (which gives us another side)

We still need an angle that is included between two sides to apply SAS. The correct choice to establish the congruence using the SAS theorem would be:

Angle F = Angle H.

This option provides the necessary included angle between the two sides we are comparing, which supports the SAS criterion. So, this is the additional piece of information required to prove that triangles EFG and HIJ are congruent by the SAS congruence theorem.

Answer 6

Wrong

Answer 7

I apologize for any confusion in my previous responses. Let's go through the information step by step again with clarity concerning your options.

You have:

• F = H (which gives us one pair of equal sides)
• E = I (which gives us another pair of equal sides)
• We need an included angle according to the SAS theorem.

Given your options for angles:

1. Angle F = Angle H
2. Angle E = Angle I
3. Angle G = Angle I
4. Angle F = Angle I

Since you need one of the angles to be included between the two sides you already have equal, we want to make sure that this angle corresponds correctly.

The correct option is:

Angle G = Angle I.

This option is critical because it states that the angle between sides E and F (which is angle E) is equal to the corresponding angle between sides H and I (which is angle I).

Therefore, to confirm the triangles are congruent by SAS, you need Angle G = Angle I. Thank you for your patience, and I hope this provides the clarity needed!

Answer 8

F=I

Answer 9

I apologize for the confusion earlier. Let's clarify the situation given that you have stated F = I.

For proving triangles EFG and HIJ are congruent by the SAS (Side-Angle-Side) theorem, you have the following pairs:

• F = H (one pair of sides)
• E = I (another pair of sides)
• G = I (this wasn't clearly stated, but if it refers to angles, please clarify)

With the additional piece of information that you are now stating is F = I, let’s see how this fits into SAS:

1. F = H gives us one pair of equal sides.
2. E = I gives us another pair of equal sides.

Now, if F = I is also true, the relevant angles need to be ruled out.

You would actually need the angles to be presented in such a way that they correspond to the sides. Here's the conclusion for the information with the new input:

1. Angle F = Angle H: there's a corresponding angle for the sides, typically needed.
2. Angle E = Angle I: This could help, depending on the triangle configurations if they were corresponding angles.

In summary, if you are saying that F = I, it leads to confusion because normally we'd expect to match corresponding vertices of the triangles.

Therefore, if you want to establish congruency by SAS, you should provide one of the angles or establish Angle F = Angle H, or ensure the relationships of the triangles are appropriately defined.

To specify, if we summarize:

Given \( F = I \) introduces a potential for confusion, please ensure the context of how these sides and angles relate, and consider using the angle that lies between the two sides equal to obtain congruence via SAS.

In conclusion, if you still want a definite angle to establish SAS congruence with initially provided options, I would go back to an angle equivalent, but specifically, I do not have a moment to clarify correct figures from F and I as sides unless specified properly. However, typically using Angle G or another specific angle included between sides should be established.

Thank you for your patience, and let me know if you need further clarification or any specific corrections!