Download PP Section 8.2

Geometry Section 8.2
Proving Triangles Similar by AA
What you will learn:
1. Use the Angle-Angle Similarity theorem
2. Solve real-life problems
To say that two polygons are similar by the
definition of similarity, we would need to
know that all corresponding sides are
_______________
proportional and all corresponding
angles are ____________.
congruent
The following theorem gives us easier
method for determining if two triangles are
similar.
Angle-Angle (AA) Similarity Theorem
If two angles of one triangle are congruent to
two angles of a second triangle, then the
triangles are similar.
Examples: Determine if the triangles are similar. If so, write a
similarity statement and identify the theorem used.
AA
EAC ~ BDC
AA
ABC ~ EDC
Similar triangles can be used to find the height of objects.
Consider these two methods.
s similar by AA
Pole' s height
Pole' s Shadow

Person' s height Person' s shadow
s similar by AA
Distance from
Tree' s height
tree to mirror

Person' s height Distance from
person to mirror
Example: Betty needs to estimate the height of a maple tree. She puts one end
of a 100-foot tape measure at the base of the tree and walks away from the tree.
At the 40-foot mark, she puts a mirror flat on the ground. Continuing to walk
away from the tree, she eventually sees the top of the tree in the mirror and
notes that she is 48 feet 8 inches away from the tree. If Betty is 5’ 3” tall,
estimate the height of the tree to the nearest foot.
5.25 8.667

tree
40
8.667tree  210
tree  24.230 ft
5.25
8.667
40
48.667
Example: Archie is 6’ 5” tall. If he casts a shadow that is 5’ 2” long at the
same time a flag pole casts a shadow 27’ 7” long, estimate the height of
the flag pole to the nearest foot.
5.167 6.417

27.583 Pole
6.417
5.167 pole  177.000
pole  34.256 ft
5.167
27.583
HW: pp 431 – 432 / 3 – 18, 21, 23 - 26