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The information given to us shows that triangles XYZ and JKL is not enough to prove they are congruent by AAS, ASA, nor SAS.
<h3>The Triangle Congruence Theorems</h3>- Two triangles are congruent by the AAS congruence theorem if they both have two pairs of congruent angles and a pair of congruent non-included sides.
- Two triangles are congruent by the ASA congruence theorem if they both have two pairs of congruent angles and a pair of congruent included sides.
- Two triangles are congruent by the SAS congruence theorem if they both have two pairs of congruent sides and a pair of congruent included angles.
Thus, the information given to us shows that triangles XYZ and JKL is not enough to prove they are congruent by AAS, ASA, nor SAS.
Learn more about triangle congruence theorem on:
General Idea:
When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.
Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.
In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.
P(x, y) becomes . We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.
Applying the concept:
The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.
Conclusion:
The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),
In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.