The student uses ratios to solve problems involving similar figures. Clarifying Activity Students use equilateral triangle pattern blocks and cubes to make generalizations about the ratios of sides, areas and volumes in similar figures using an activity like the one below. Use other pattern block shapes to investigate other similar polygons in the same manner as described in Question 1 and record your findings in the table below. Based on your investigations in Questions 1 and 2, make a generalization. B. Explore relationships between the investigations in Question 1 and the Sierpinski triangle.
P throws out a beam of light.
The light shines on a screen that can be moved closer to or farther from the light. B. The lengths a and b indicate the lengths of the light patch on the screen. Show that the ratio of the length b to the length a depends only on the distances A and B, and not on the angle y that the beam is off the perpendicular, nor on the angle x the beam itself makes. It is the scale factor relating the distances of the two screens, and the sizes of the images on the two screens. The student applies the concepts of similarity to justify properties of figures and solve problems.