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Question 1

A)What does the SAS Congruence Theorem say?(1 point)
Responses

If a triangle has an angle between two congruent sides, then it is isosceles.
If a triangle has an angle between two congruent sides, then it is isosceles.

If two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent.
If two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent.

If two triangles have one pair of congruent angles and at least one pair of congruent sides, then the triangles are congruent.
If two triangles have one pair of congruent angles and at least one pair of congruent sides, then the triangles are congruent.

If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.
If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.
Question 2
A)Which of the following pairs of triangles could you use to justify that the SAS Congruence Theorem is true?(1 point)
Responses

An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I.

An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E F is congruent to side H I. Angle F is congruent to angle I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E F is congruent to side H I. Angle F is congruent to angle I. Angle E is congruent to angle H.

An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E G is congruent to side H J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E G is congruent to side H J. Side E F is congruent to side H I. Angle E is congruent to angle H.

An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Question 3
A)Which of the following pairs of triangles illustrate the SAS criterion for triangle congruence?(1 point)
Responses

Two congruent triangles positioned side by side in the same orientation.
Image with alt text: Two congruent triangles positioned side by side in the same orientation.

Two congruent triangles.
Image with alt text: Two congruent triangles.

Two congruent triangles
Image with alt text: Two congruent triangles

Two congruent triangles.
Image with alt text: Two congruent triangles.
Question 4
A)
Use the image to answer the question.

A rhombus A B C D. From the top, clockwise, the vertices are A, D, C, and B.

If you wanted to explain why △ABD≅CBD by the SAS Congruence Theorem, which of the following would be helpful to know?

(1 point)
Responses

AC¯¯¯¯¯¯¯¯ is the angle bisector of ∠BCD.
Modifying above upper A upper C with bar is the angle bisector of angle upper B upper C upper D .

BD¯¯¯¯¯¯¯¯ is the angle bisector of ∠ABC.
Modifying above upper B upper D with bar is the angle bisector of angle upper A upper B upper C .

AC¯¯¯¯¯¯¯¯ is the angle bisector of ∠BAD.
Modifying above upper A upper C with bar is the angle bisector of angle upper B upper A upper D .

BD¯¯¯¯¯¯¯¯ is the angle bisector of ∠BCD.
Modifying above upper B upper D with bar is the angle bisector of angle upper B upper C upper D .
Question 5
A)
Use the image to answer the question.

Two congruent triangles in different orientations, one next to the other. Triangle A B C is on the left, and triangle L M N is on the right.

Are the triangles congruent? If so, write a congruence statement and reason why.

(1 point)
Responses

Yes, △ABC≅△LMN by the SSA Congruence Theorem.
Yes, triangle upper A upper B upper C congruent to triangle upper L upper M upper N by the SSA Congruence Theorem.

Yes, △ABC≅△MLN by the SSA Congruence Theorem.
Yes, triangle upper A upper B upper C congruent to triangle upper M upper L upper N by the SSA Congruence Theorem.

No, the triangles are not necessarily congruent.

1 answer

Here are the responses to your questions based on the SAS Congruence Theorem and triangle congruence concepts:

Question 1:
A) What does the SAS Congruence Theorem say?
Response:
If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.

Question 2:
A) Which of the following pairs of triangles could you use to justify that the SAS Congruence Theorem is true?
Response:
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I.

Question 3:
A) Which of the following pairs of triangles illustrate the SAS criterion for triangle congruence?
Response:
Two congruent triangles positioned side by side in the same orientation.

Question 4:
A) If you wanted to explain why △ABD≅CBD by the SAS Congruence Theorem, which of the following would be helpful to know?
Response:
AC is the angle bisector of ∠BCD.

Question 5:
A) Are the triangles congruent? If so, write a congruence statement and reason why.
Response:
No, the triangles are not necessarily congruent.

These answers align with the principles of triangle congruence, specifically the application of the SAS theorem. If you have any more questions or need further clarification, feel free to ask!