Transcript 7.4 A Postulate for Similar Triangles

7.3
Proving Triangles Similar
-AA Similarity
-SSS Similarity
-SAS Similarity
• We can prove that 2 triangles are similar by
showing that all 3 corresponding angles are
congruent, and all 3 sides are in proportion to
one another (same as showing any 2 polygons
similar)
• But there are simpler methods to prove 2
triangles similar.
AA Similarity Postulate
• If two angles of one triangle are congruent to
two angles of another triangle, then the triangles
are similar.
Are these triangles
similar, if so, then
why? Can you find x?
And AE and ED? What
is the scale factor?
SAS Similarity Theorem
• If an angle of one triangle is congruent to an
angle in another triangle and the sides including
those angles are in proportion, then the triangles
are similar.
http://www.mathopenref.com/similarsas.html
• Use the given lengths to prove that
∆RST ~ ∆PSQ.
Given: SP=4, PR = 12,
SQ = 5, and QT = 15;
S
4
P
12
R
5
Q
Prove: ∆RST ~ ∆PSQ
15
T
SSS Similarity
• If all the sides of two triangles are in proportion,
then the triangles are similar.
http://www.mathopenref.com/similarsss.html
What do x and y have to be in order for these 2 triangles
to be similar by SSS?
A
6
B
x
E
y
C
15.2
D
What similarity do these
2 triangles have?
• A very common class of exercises is finding the
height of something very tall by using the
daytime shadow length of that same thing, its
shadow being down along the ground, and thus
easily accessible and measurable. You use the
known height of something shorter, along with
the length of its daytime shadow as measured at
the same time.
• A building casts a 103-foot shadow at the
same time that a 32-foot flagpole casts as
34.5-foot shadow. How tall is the
building? (Round your answer to the
nearest tenth.)
• Nate and Sam are visiting Washington D.C.
They want to know the height of the Washington
Monument. The monument’s shadow is 111 feet
at the same time that Sam’s shadow is 1 foot.
Sam is 5 feet tall.