Unit 1, Lesson 11
¿Qué es igual?
Grado 8
11.1
Warm-up
Encuentra las manos derechas
Las manos de una persona son imágenes de espejo una de la otra. En el diagrama hay una mano izquierda marcada. Colorea todas las manos derechas.
11.2
Activity
¿Son iguales?
En cada pareja de figuras, decide si son iguales o no.
Five pairs of figures, A, B, C, D and E. Figure A shapes match, the shape on the right is the image of the left shape after a reflection and translation. Figure B shapes do not match, they have congruent sides but angle measures do not match. Figure C shapes match, the shape on the left is the image of the left shape after a reflection. Figure D shapes do not match, the shape on the left is bigger. Figure E shapes do not match, the puzzle shape on the right has a lower right side part tab than the same tab of the left puzzle shape.
Five pairs of figures, A, B, C, D and E. Figure A shapes match, the shape on the right is the image of the left shape after a reflection and translation. Figure B shapes do not match, they have congruent sides but angle measures do not match. Figure C shapes match, the shape on the left is the image of the left shape after a reflection. Figure D shapes do not match, the shape on the left is bigger. Figure E shapes do not match, the puzzle shape on the right has a lower right side part tab than the same tab of the left puzzle shape.
Five pairs of figures, A, B, C, D and E. Figure A shapes match, the shape on the right is the image of the left shape after a reflection and translation. Figure B shapes do not match, they have congruent sides but angle measures do not match. Figure C shapes match, the shape on the left is the image of the left shape after a reflection. Figure D shapes do not match, the shape on the left is bigger. Figure E shapes do not match, the puzzle shape on the right has a lower right side part tab than the same tab of the left puzzle shape.
Five pairs of figures, A, B, C, D and E. Figure A shapes match, the shape on the right is the image of the left shape after a reflection and translation. Figure B shapes do not match, they have congruent sides but angle measures do not match. Figure C shapes match, the shape on the left is the image of the left shape after a reflection. Figure D shapes do not match, the shape on the left is bigger. Figure E shapes do not match, the puzzle shape on the right has a lower right side part tab than the same tab of the left puzzle shape.
Five pairs of figures, A, B, C, D and E. Figure A shapes match, the shape on the right is the image of the left shape after a reflection and translation. Figure B shapes do not match, they have congruent sides but angle measures do not match. Figure C shapes match, the shape on the left is the image of the left shape after a reflection. Figure D shapes do not match, the shape on the left is bigger. Figure E shapes do not match, the puzzle shape on the right has a lower right side part tab than the same tab of the left puzzle shape.
11.3
Activity
Área, perímetro y congruencia
- ¿Cuáles de estos rectángulos tienen la misma área que el rectángulo R pero distinto perímetro?
- ¿Cuáles rectángulos tienen el mismo perímetro que el rectángulo R pero distinta área?
- ¿Cuáles tienen la misma área y el mismo perímetro que el rectángulo R?
- Decide cuáles rectángulos son congruentes. Usa el mismo color para colorear los rectángulos congruentes.
Student Lesson Summary
Congruente es un nuevo término para una idea que ya hemos usado. Decimos que dos figuras son congruentes si una se puede alinear exactamente con la otra por medio de una transformación rígida.
Por ejemplo, el triángulo
Triangle A B C, triangle A B prime C, dashed arrow from B prime to point F and triangle E F D. Triangle A B prime C is the image of triangle A B C after reflection over A C. Angle A is 63 point 4 degrees, angle B is 71 point 6 degrees and angle C is 45 degrees. Side A B is 2 point 2 4, side B C is 2 point 8 3 and side A C is 3 point 0 0. Angle E is 63 point 4 degrees, angle F is 71 point 6 degrees and angle D is 45 degrees. Side E F is 2 point 2 4, side F D is 2 point 8 3 and side D E is 3 point 0 0.
Estos son otros hechos sobre figuras que son congruentes:
- No debemos revisar todas las medidas para probar que dos figuras son congruentes. Solo tenemos que encontrar una transformación rígida que haga coincidir las figuras.
- Una figura que parece una imagen de espejo de otra figura puede ser congruente a esta. Esto significa que debe haber una reflexión en la secuencia de transformaciones que hace coincidir las figuras.
- Los polígonos congruentes tienen la misma área y el mismo perímetro. Por eso, una manera de demostrar que dos polígonos no son congruentes es verificar que su área o su perímetro son distintos.
congruente
Una figura es congruente a otra si puede moverse con traslaciones, rotaciones y reflexiones para coincidir exactamente con la otra.
En la figura, el triángulo A es congruente a los triángulos B, C y D.
- Una traslación lleva al triángulo A al triángulo B.
- Una rotación lleva el triángulo B al triángulo C.
- Una reflexión lleva el triángulo C al triángulo D.
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