By Laurent Bessieres, Gerard Besson, Michel Boileau
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Extra resources for Geometrisation of 3-Manifolds (EMS Tracts in Mathematics)
Which enlargements are similar in shape? b. Wanda places an order for an enlargement to be similar to the 18 ؋ 27 size, with a width of 27 cm. What will the length of her enlargement be? Painters often paint very high walls and ceilings. To make the job easier, the painters connect two large ladders with a board so they do not have to walk up and down one ladder. They walk across the raised board to paint the higher spots. Suppose each ladder has the same number of steps. The painter puts a board resting on the third step on either side.
Now compare ᭝ABC and ᭝DFC. Is ᭝ABC ϳ ᭝DFC? Give an explanation. c. What do you think makes triangles similar? 4. a. What is the multiplication factor for ᭝DEC and ᭝ABC? b. ” Explain whether you agree or disagree with Bill. In problems 1–4, you investigated when two triangles might be similar. You began with two pairs of corresponding sides having a multiplication factor of 3. The triangles were similar, sides formed parallel lines, and corresponding angles had the same measure. 75, not 3. The triangles were NOT similar.
What type of triangle are the glass plates? 9. Use the net for this building on Student Activity Sheet 5. a. Show where you expect each of the floors to meet the glass plates by drawing floor lines on the net. b. Cut out the net. Fold it so the triangles show on the outside. c. Find the area of each of the three floors of the building. Explain how you found your answer. Suppose a floor is halfway between the ground floor and the top of the pyramid. Tell whether each statement is true and explain your answers.
Geometrisation of 3-Manifolds (EMS Tracts in Mathematics) by Laurent Bessieres, Gerard Besson, Michel Boileau