Sketch two triangles. label the lengths of the sides of triangle a as 3, 4, and 5. label the lengths of the sides of triangle b as 5, 12, and 13. a. what is the sum of the measures of the acute angles of any right triangle? explain your reasoning. b. write the tangent ratios for the acute angles of triangle a. c. write the tangent ratios for the acute angles of triangle b. d. write a rule describing the relationship between the tangents of the acute angles of any right triangle.

Part a what is the area of triangle i? show your calculation. part b triangles i and ii are congruent (of the same size and shape). what is the total area of triangles i and ii? show your calculation. part c what is the area of rectangle i? show your calculation. part d what is the area of rectangle ii? show your calculation. part e rectangles i and iii have the same size and shape. what is the total area of rectangles i and iii? show your calculation. part f what is the total area of all the rectangles? show your calculation. part g what areas do you need to know to find the surface area of the prism? part h what is the surface area of the prism? show your calculation. part i read this statement: “if you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” is this statement true or false? why? part j read this statement: “if you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” is this statement true or false? why?