Transcript lesson 1.9
SECTION 1-9 A PICTURE IS WORTH A 1000 WORDS A picture is worth a thousand words. This expression certainly apples to geometry. A drawing of an object often conveys information more quickly than a long written description. Visualization skills are extremely important in Geometry. To visualize a plane you picture a flat surface. In another lesson you visualized the number of ways four lines can intersect. Can you picture what the hands of a clock look like at 3:30? Volumes 1 and 2 of a twovolume set sit next to each other on a shelf. The sit in the proper order: Volume 1 is on the left and Volume 2 is on the right. Each front cover is 1/8 inch thick and the page portion of each book is 1 inch. If a bookworm starts at the first page of Volume 1 and burrows all the way to the last page of Volume 2, how far did it travel? 1 2 Did the bookworm eat 2 ¼”? Seems reasonable. The bookworm ate only through the two covers or ¼” Harold, Dina, and Linda are standing of a flat, dry field reading their treasure map. Harold is standing at one of the features marked on the map, a gnarled tree stump, and Dina is standing atop a large black boulder. The map shows that the treasure is buried 60 meters from the tree stump and 40 meters from the large black boulder. Harold and Dina are standing 80 meters apart. What is the locus of points (or all possible locations) where the treasure might be buried. 60 m 40 m 80 m Possible locations for the treasure A diagram can also help organize information to help make sense of difficult concepts. A Venn diagram represents larger groups that contain smaller groups such as circle within circle, or ovals within ovals. Weekday Activities Weekend Activities Can you think of activities that would fit in each section of the circles? EXAMPLE Create a Venn diagram to show the relationships among parallelograms, rhombuses, rectangles, and squares. What is the most general group? Parallelograms What do all four shapes have in common? NOW CONSIDER THE SPECIAL CHARACTERISTICS OF RHOMBUSES, RECTANGLES AND SQUARES Rhombus: 4 congruent sides or equilateral Rectangle: 4 congruent angles or equiangular Square: 4 congruent sides and 4 congruent angles Or both equilateral and equiangular Let’s add ovals for the other figures: rhombuses, rectangles and squares Parallelograms Rhombus Square Rectangle What do all four shapes have in common?