Download Advanced Geometry LT 5.1 Identify similar triangles and use

Advanced Geometry LT 5.1
Identify similar triangles and use proportions and
triangle properties to solve and justify solutions to
problems
Draw a triangle with angles of
Measure the side lengths.
and
,
.
,
Compare your side lengths to those of your group members. Are they the same? Is there any relationship?
Try making ratios with your side lengths. Which sides will you match up?
What do you notice about the ratios? What does this mean?
Similar Polygons
Polygons (figures) with corresponding angles congruent and corresponding side lengths that are proportional.
What does this mean?
Example 1: Are the figures similar?
a)
b)
Example 2:
Each pair of polygons is similar. Write a similarity statement, then find the missing variable(s).
a)
b)
Angle-Angle Triangle Similarity (AA~) Theorem
If two triangles of one triangle are congruent to two angles of another triangle, then the two triangles are
similar.
Why don’t we need to know all 3 angles are congruent?
Side-Side-Side Triangle Similarity (SSS~) Theorem
If the three sides of one triangle are proportional to the corresponding sides of another triangle, then the
triangles are similar.
Side-Angle-Side Triangle Similarity (SAS~) Theorem
If two sides of one triangle are proportional to the corresponding sides of another triangle, and their included
angles are congruent, then the triangles are similar.
Why isn’t ASA~ a theorem?
Example 3:
Determine whether each pair of triangles is similar. Justify your answer.
a)
b)
c)
d)
Example 4:
Each pair of triangles is similar. Find x and y.
a)
b)
c)
c)
Example 5:
Find all possible values of x for which these two triangles are similar.
Example 6:
Identify two similar triangles in the figure, and explain why they are similar. Then find AB.