1. Muestra que los dos pentágonos del diagrama son congruentes.

   

   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. Encuentra las longitudes de los lados del pentágono \(ABCDE\) y las medidas de los ángulos del pentágono \(FGHIJ\).

Para cada pareja de figuras, decide si las dos figuras son o no congruentes. Explica tu razonamiento.

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.

1. Dibuja el segmento \(PQ\).
2. Cuando \(PQ\) se rota \(180^\circ\) alrededor del punto \(R\), el segmento que resulta es el mismo que \(PQ\). ¿Dónde podría estar ubicado el punto \(R\)?

Este es un trapecio.

Usando transformaciones rígidas sobre el trapecio, construye un patrón. Describe algunas de las transformaciones rígidas que usaste.