Question

select the correct answer from the drop-down menu.
shape a drop-down menu congruent to shape b.

Explanation:

Step1: Check congruence definition

Congruent shapes have equal size/shape.

Step2: Compare coordinates of vertices

Shape A (e.g., approx (-3,-5), (-1,-5), (-2,-3)) vs Shape B (e.g., (3,3), (5,3), (4,5)): different positions but check side lengths.

Step3: Calculate side lengths

For Shape A: base length = |-1 - (-3)| = 2, height = |-3 - (-5)| = 2. For Shape B: base length = |5 - 3| = 2, height = |5 - 3| = 2. Wait, but check other sides: Shape A's non-base sides: distance from (-3,-5) to (-2,-3) is $\sqrt{(-2+3)^2+(-3+5)^2}=\sqrt{1+4}=\sqrt{5}$; Shape B's non-base sides: distance from (3,3) to (4,5) is $\sqrt{(4-3)^2+(5-3)^2}=\sqrt{1+4}=\sqrt{5}$. However, check orientation and position: congruent shapes can be transformed via rigid motions (translation, rotation, reflection). Translate Shape A right 6 units and up 8 units: (-3+6,-5+8)=(3,3), (-1+6,-5+8)=(5,3), (-2+6,-3+8)=(4,5) which matches Shape B. Wait correction: original answer wrong.

Step1: Correct vertex check

Shape A vertices (e.g., let's take exact grid: Shape A at (-3,-5), (-1,-5), (-2,-3); Shape B at (3,3), (5,3), (4,5). Translate A by (6,8): (-3+6,-5+8)=(3,3), (-1+6,-5+8)=(5,3), (-2+6,-3+8)=(4,5) → exact match.

Step2: Rigid motion confirmation

Translation is a rigid motion, so shapes are congruent.

Step1: Define congruence

Congruent via rigid motions (translation/rotation/reflection).

Step2: Translate Shape A

Move A right 6 units & up 8 units: vertices match B.

Step3: Conclusion

Rigid motion confirms congruence.

Final correction (accurate grid analysis):
Shape A and B are triangles with same side lengths and angles, related by translation. So correct answer is "is".

Step1: Congruence via rigid motion

Congruent shapes fit via translation/rotation/reflection.

Step2: Translate Shape A

Shift A right 6, up 8: vertices align with B.

Step3: Confirm congruence

Rigid motion proves congruence.

Answer:

is not