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

Question

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

(1 point)
Responses

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 .

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 .

AC¯¯¯¯¯¯¯¯
is the angle bisector of ∠BCD
.

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

(1 point)
Responses

No, the triangles are not necessarily congruent.
No, the triangles are not necessarily congruent.

Yes, △ABC≅△LNM
by the SAS Congruence Theorem.
Yes, triangle cap A cap b cap c is congruent to triangle cap l cap n cap m by the SAS Congruence Theorem.

Yes, △ABC≅△LMN
by the SAS Congruence Theorem.
Yes, triangle cap A cap b cap c is congruent to triangle cap l cap m cap n by the SAS Congruence Theorem.

Yes, △ABC≅△MLN
by the SAS Congruence Theorem.
Yes, triangle cap A cap b cap c is congruent to triangle cap m cap l cap n by the SAS Congruence Theorem.

Answer 1

The SAS Congruence Theorem states:

If two triangles have one pair of congruent sides and the included angle between those sides is congruent, then the triangles are congruent.

Now, regarding the other parts of your question:

1. To explain why △ABD ≅ △CBD by the SAS Congruence Theorem, you would need to know:

   BD is the angle bisector of ∠BCD.

   This information indicates that the two triangles share the side BD and the corresponding angles and sides can be compared.

2. For the question "Are the triangles congruent? If so, write a congruence statement and reason why," it would depend on the specific conditions given for triangles ABC and LMN. However, based on what was provided:

   Yes, △ABC ≅ △LMN by the SAS Congruence Theorem.

   This is true if you have one pair of congruent sides included with a congruent angle.

Thus, the correct statements regarding the SAS theorem and the congruences above would be:

• Quadrant 1: The SAS Congruence Theorem definition.
• Quadrant 2: BD is the angle bisector of ∠BCD.
• Quadrant 3: Yes, △ABC ≅ △LMN by the SAS Congruence Theorem.