Transcript File

Similar Triangles
Geometry
ANGLE-ANGLE SIMILARITY POSTULATE
(AA~)
If two angles of one triangle are congruent to
two angles of another triangle, then the two
triangles are similar.
SIDE-SIDE-SIDE (SSS~)
SIMILARITY THEOREM
If the corresponding sides of two triangles are
proportional, then the triangles are similar.
SIDE-ANGLE-SIDE (SAS~)
SIMILARITY THEOREM
If an angle of one triangle is congruent to an
angle of a second triangle and the lengths of
the sides including these angles are
proportional, then the triangles are similar.
Determine whether the triangles
are similar. If so, write a similarity
statement. Explain your reasoning.
Determine whether the triangles
are similar. If so, write a similarity
statement. Explain your reasoning.
Determine whether the triangles
are similar. If so, write a similarity
statement. Explain your reasoning.
Determine whether the triangles
are similar. If so, write a similarity
statement. Explain your reasoning.
Determine whether the triangles
are similar. If so, write a similarity
statement. Explain your reasoning.
Example
In the figure, ∠ADB is a right angle. Which of
the following would not be sufficient to prove
that ∆ADB ~ ∆CDB?
Properties of Similarity
Similarity is Reflexive, Symmetric, and Transitive!
Example
Find BE and AD.
Example
Find QP and MP.
Example
Find WR and RT.
Example
You are at an indoor climbing wall. To estimate
the height of the wall, you place a mirror on the
floor 85 feet from the base of the wall centered
in the mirror. You are 6.5 feet from the mirror
and your eyes are 5 feet above the ground. Use
similar triangles to estimate the height of the
wall.
Example
Hallie is estimating the height of the Superman
roller coaster in Mitchellville, Maryland. She is 5
feet 3 inches tall and her shadow is 3 feet long.
If the length of the shadow of the roller coaster
is 40 feet, how tall is the roller coaster?
Example
At another indoor climbing wall, a person whose
eyes are 6 feet from the floor places a mirror on
the floor 60 feet from the base of the wall. They
then walk backwards 5 feet before seeing the
top of the wall in the center of the mirror. Use
similar triangles to estimate the height of this
wall.
Example
Adam is standing next to the Palmetto Building
in Columbia, South Carolina. He is 6 feet tall and
the length of his shadow is 9 feet. If the length
of the shadow of the building is 322.5 feet, how
tall is the building?