TRIANGLES AND PATCHWORK

GOALS

1. Identify congruent and similar figures

2. Recognize and use patterns in arrangements of congruent triangles

3. Identify corresponding sides in similar triangles

4. use a strategy to find the multiplier

5. determine unknown lengths in given similar triangles

6. understand the relationship between parallel lines and equal angles

7. prove that two triangles are similar

8. use properties of similar triangles to solve problems

9. choose appropriate models and tools to solve geometrical problems

10. reason about and use the concepts of ratios and similarity in solving problems

SECTION SUMMARIES

SECTION A: PATCHWORK

1. Congruent figures have the same shape and size.

2. When you make a large triangle from rows made of congruent triangles, two things happen; rows form parallel

lines in three different directions, and there are the same number of small triangles along each edge.

SECTION B: TESSELLATIONS

1. You can find the lengths of the sides of a small triangle if you know all three lengths in the large triangle and the number of small triangles that fit along each edge.

2. You can find the lengths of the sides of the large triangle if you know all three lengths of the small triangle and the number of triangles that fit along each edge of the large triangle.

SECTION C: USING MULTIPLIERS

1. In similar figures, if the lengths of two corresponding sides are know, the multiplier can be found and then used to find the lengths of other sides of the figures.

2. When solving a problem, begin by making a drawing and labeling the side lengths that are known; then look for similar figures.

3. Two methods for solving for a missing side(s) similar triangles (figures) …

· Sketch the two triangles drawing arrows to show corresponding sides, then find the multiplier & use it.

· Make a ratio table for the corresponding sides, then use the ratio table.

4. The strategy of solving proportions can also be used. Set up two equal ratios comparing the sides of the figure,

then cross-multiply and solve the resulting equation.

SECTION D: WHEN TRIANGLES ARE SIMILAR

1. You can conclude that triangles are similar if:

· all pairs of corresponding sides in the two triangles have the same ratio, or

· two pairs of corresponding angles are equal.

SECTION E: MIXED PROBLEMS

1. In this section, you solved problems using similar triangles, ratios of sides, and multipliers.