1. Quick Start Expectations d 135⁰ d 45⁰ Teaching Target: I can use rep-tiles to see the effect of scale factor on side lengths, angles, perimeter, and area. Packet HW: 1) Inv. 3-4 pg. 4 – Similar Rectangles 2) Math XL – 20 mins this week Warm-Up For each of the following angle measures, find the measure of its supplementary angle.

3. video

4. Multiple squares form a larger square. Multiple hexagons do NOT form a larger hexagon.

5. How do rep-tiles show that the scale factors and areas of similar quadrilaterals and triangles are related?

6. As a table group work on Inv. 3-4 p. 2-3: Not similar Similar! Scale factor: 3 Scale factor: 2

7. original nine copies scale factor = 3 scale factor x scale factor = area 9 x 9 = 81 in² 15 x 9 = 135 in² √ 81 = 9 in² 3 x 3 = 9 ut² 9 in²

8. scale factor x scale factor = area scale factor = 5 4 x 25 = 100 cm² 4 cm² 5 x 5 = 25 ut² 225 ÷ 25 = 9 cm² 9 cm²

9. Not similar Similar! Scale factor: 2 Similar! Not similar

10. Packet HW: 1) Inv. 3-4 pg. 4 – Similar Rectangles 2) Math XL – 30 mins this week

11. Additional practice: Each side length of the larger is twice the length of the corresponding side of the smaller triangle. (2 x 1 = 2 ) original four copies scale factor 1 scale factor 2 The perimeter of the larger is twice the perimeter of the smaller (for a scale factor of 2). (2 x 4 = 8 ut ) The area is 4 times the area of the original because four of the smaller triangles fit into the larger triangle. This is also the square of the scale factor. (2² x 1 = 4 ut²)

12. The side lengths of the new rep-tile A is twice (2x) the corresponding sides of the original. (2 x 1 = 2) scale factor 1 scale factor 2 scale factor 4 B is four times (4x) the corresponding sides of the original. (4 x 1 = 4) And is twice (2x) the sides of A. (2 x 2 = 4) B A original

13. side length: area: perimeter: angles: The scale factor (4) times the corresponding side length of the small rectangle (1) (4 x 1 = ) For this example: The perimeter of the large rectangle is the scale factor (4) times the perimeter of the small rectangle (4) (same) (4 x 4 = ) Angles of all similar figures are congruent, no matter what the scale factor is. (4² x 1 = ) The square of the scale factor (4²) times the area of the small rectangle (1). 4 16 ut 16 ut²

14. original trapezoid Sketch non-rectangular parallelogram parallelogram four copies Sketch these figures. Then try to form a rep-tile out of each. Yes! All rectangles & parallelograms have copies that can fit together to make a larger shape that is similar to the original. Can you form a rep-tile out of each of these shapes?

15. p. 54 Sketch one of these figures. Then try to form a rep-tile. Can you form a rep-tile out of each of these shapes? Yes! All triangles (right, isosceles, and scalene) have copies that can fit together to make a larger, similar triangle. A scalene triangle and rep-tile

16. scale factor 1 scale factor 2 The perimeter of the larger triangle is twice the perimeter of the smaller triangle (for a scale factor of 2). Each side length of the larger triangle is twice the length of the corresponding side of the smaller triangle. The area is 4 times the area of the original because four of the smaller triangles fit into the larger triangle. This is also the square of the scale factor. (2 x 1 = 2 ) (2 x 3 = 6 ut ) (2² x 1 = 4 )

17. scale factor 4 scale factor 1 scale factor 2 2. Find the scale factor of the largest rep-tile.

18. side length: perimeter: angles: area: The scale factor (4) times the side lengths of the smaller triangle (1). (4 x 1 = ) 4 (4 x 3 = ) The scale factor (4) times the perimeter of the smaller triangle (3). 12 ut The same! The square of the scale factor (4²) times the area of the smaller triangle (1). (4² x 1 = ) 16 ut²