Lección 14
Ángulos alternos internos
Exploremos por qué algunos ángulos siempre son iguales.
Problema 1
Usa el diagrama para encontrar las medidas de cada ángulo.
- \(m{\angle ABC}\)
- \(m{\angle EBD}\)
- \(m{\angle ABE}\)
![Two lines, line E C and line A D, that intersect at point B. Angle C B D is labeled 45 degrees.](https://staging-cms-im.s3.amazonaws.com/5ZyMLomGE6YoMm3pmEMVXaaS?response-content-disposition=inline%3B%20filename%3D%228.1.D.PP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278.1.D.PP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141459Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=31b6ac1d984d3778bca245da9f5644579f2887c7c42fdf7eb5f25134cfd976ae)
Problema 2
Las rectas \(k\) y \(\ell\) son paralelas y la medida del ángulo \(ABC\) es 19 grados.
![Two parallel lines, k and l, cut by transversal line m.](https://staging-cms-im.s3.amazonaws.com/DEJUC5fkJ5jfMnzU5gjdQA85?response-content-disposition=inline%3B%20filename%3D%228-8.1.B.PP.Image.12.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.B.PP.Image.12.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141459Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=32e02d3eaf497664b2f45442f03e5d8b00daacb24d31991ec143d3e91b4986b8)
- Explica por qué la medida del ángulo \(ECF\) es 19 grados. Si se te dificulta, considera trasladar la recta \(\ell\) moviendo \(B\) a \(C\).
- ¿Cuál es la media del ángulo \(BCD\)? Explica.
Problema 3
El diagrama muestra tres líneas con algunas medidas de ángulos etiquetadas.
![Two lines that do not intersect. A third line intersects with both lines.](https://staging-cms-im.s3.amazonaws.com/23cy1uwuxU8NDj2Eb5D4jMR8?response-content-disposition=inline%3B%20filename%3D%228-8.1.D14.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.D14.newPP.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141459Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ac02b2dacab27e9f653d00fc588761f9db304e6b6015f1365e505e8a490561ba)
Encuentra las medidas de los ángulos que faltan que están etiquetadas signo de interrogación.
Problema 4
Las rectas \(s\) y \(t\) son paralelas. Halla el valor de \(x\).
![Four lines. Two parallel lines are labeled s and t. Two other lines that intersect at a right angle at a point on line t. One angle is labeled 40 degrees. Another angle is labeled x degrees.](https://staging-cms-im.s3.amazonaws.com/C7VehJtgLrE7Ymp34nvB1iAG?response-content-disposition=inline%3B%20filename%3D%22angle%20diagram.png%22%3B%20filename%2A%3DUTF-8%27%27angle%2520diagram.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141459Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b8f810f474e132bf6cb0e415b5e910fbddafc17e17583dae6bc7b11ee87b0aa9)
Problema 5
Las dos figuras son copias a escala entre sí.
- ¿Cuál es el factor de escala que lleva la Figura 1 a la Figura 2?
- ¿Cuál es el factor de escala que lleva la Figura 2 a la Figura 1?
![Two quadrilaterals on a grid.](https://staging-cms-im.s3.amazonaws.com/zxdcvdtii1bvfcqe0qwa6aahdp05?response-content-disposition=inline%3B%20filename%3D%228.1.PP.7Grev6_es.png%22%3B%20filename%2A%3DUTF-8%27%278.1.PP.7Grev6_es.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141459Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e24f6f0208b382ff31e77ef339d12fd894471baaa6edad367e64fac3e77f6428)