Question

Prove that AABC is congruent to ADEF with the given vertices are congruent. A(3,1), B (4,5), C (2, 3), D(-1, -3), E (-5, -4), F (-3,-2) A. The triangles are congruent because AABC can be mapped onto ADEF by a rotation: (x,y) → (y,x), followed by a reflection: (x,y) → (x,-y) B. The triangles are congruent because AABC can be mapped onto ADEF by a reflection: (x,y) → (x,y), followed by a rotation: (x,y) → (y, -x). C. The triangles are congruent because AABC can be mapped onto ADEF by a translation: (x, y) = (x-4, y), followed by another translation: (x, y) = (x,y-). D. The triangles are congruent because AABC can be mapped onto ADEF by a rotation: (x, y) = (-y, x), followed by a reflection: T(x,y) → (x,-y).

Answer 1

The triangles AABC and ADEF can be proven to be congruent using the SAS (Side-Angle-Side) congruence criterion.

Step-by-step explanation:

The triangles AABC and ADEF can be proven to be congruent using the SAS (Side-Angle-Side) congruence criterion. In this case, we can use the congruence of the corresponding sides AB and DE, BC and EF, and the included angle at vertex A.

Using the given coordinates, we can calculate the lengths of the sides and the measures of the angles to verify the congruence.

For example, the distance between A(3,1) and B(4,5) can be found using the distance formula: AB = sqrt((4-3)^2 + (5-1)^2) = sqrt(1^2 + 4^2) = sqrt(1 + 16) = sqrt(17).