1. Show that the two pentagons in the following image are congruent.

   

   Two figures A B C D E and F G H I J on a square grid. Let the lower left corner be (0 comma 0). Then A B C D E has coordinates A(2 comma 3), B(1 comma 5), C(2 comma 6), D(5 comma 5) and E(4 comma 1) and F G H I J has coordinates F(7 comma 3), G(11 comma 2), H(12 comma 5), I(11 comma 6) and J(9 comma 5). For figure A B C D E, angle A is 162 degrees, angle B is 108 degree, angle C is 117 degrees, angle D is 94 degrees and angle E is 59 degrees. For figure F G H I J, side F G is 4 point 1, side G H is 3 point 2, side H I is 1 point 4, side I  J is 2 point 2 and side J F is 2 point 8. Figure J I H G F appears to be the image of figure A B C D E after a rotation and a translation.

2. Find the side lengths of pentagon \(ABCDE\) and the angle measures of pentagon \(FGHIJ\).

These two figures are congruent and have corresponding points marked.

1. Are angles \(ABC\) and \(A'B'C'\) congruent? Explain your reasoning.
2. Measure angles \(ABC\) and \(A’B’C’\) to check your answer.

For each pair of shapes, decide whether or not the two shapes are congruent. Explain your reasoning.

1.  

   

   Two quadrilaterals A B C D and E F G H on a square grid. Let the lower left corner be (0 comma 0). Then the coordinates of A B C D are A(1 comma 3), B(2 comma 4), C(2 comma 5)and D(5 comma 5). The coordinates of E F G H are E(11 comma 1), F(10 comma 2), G(10 comma 3)and H(6 comma 3).

2.  

   

   Two figures A B C D E F and G H I J K L on a coordinate plane, origin O. Horizontal axis scale negative 7 to 6 by 1’s. Vertical axis scale negative 3 to 4 by 1’s. The coordinates of A B C D E F are A(negative 6 comma 2), B(negative 4 comma 2), C(negative 4 comma negative 2 ), D(negative 2 comma 3), E(negative 4 comma 4) and F(negative 7 comma 4 ). The coordinates of G H I J K L are G(0 comma negative 1), H(5 comma negative 3), I(6 comma negative1), J(6 comma 2), K(4 comma 1) and L(4 comma 0).

3.  

   

   Two circles A and C on a coordinate plane, origin O. Horizontal axis scale negative 8 to 7 by 1’s. Vertical axis scale negative 4 to 5 by 1’s. The center of circle A is A(negative 4 comma 2). The center of circle C is C(4 comma negative 1). Both circles have a diameter of 2.

Which of these four figures is congruent to this figure?