Question

Please look at the image below. By the way this is my homework.Use the definition of congruence to decide whether the two figures are congruent. Explain your answer. Give coordinate notation for the transformations you use.

Answer 1

Congruent Shapes

Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),

All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.

The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.

Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is

xm = (-6+4)/2 = -1

Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:

xm = (-8+6)/2 = -1

For the points R(-4,-6) and D(2,-6):

xm = (-4+2)/2 = -1

For the points Q(-9,-4) and D(8,-4):

xm = (-9+8)/2 = -0.5

Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent

For both shapes to be congruent, the coordinates of Q should have been (-10,-4)