Similar Triangles I

Download Report

Transcript Similar Triangles I

Click one of the buttons below
or press the enter key
BACK
NEXT
EXIT
In geometry, two polygons
are similar when one is a
replica (scale model) of
the other.
BACK
NEXT
EXIT
Consider Dr. Evil and Mini Me from
Mike Meyers’ hit movie Austin Powers.
Mini Me is supposed to be an exact
replica of Dr. Evil.
BACK
NEXT
EXIT
BACK
NEXT
EXIT
The following are similar figures.
I
II
BACK
NEXT
EXIT
The following are non-similar figures.
I
II
BACK
NEXT
EXIT
Feefee the mother cat, lost her daughters, would you
please help her to find her daughters. Her daughters have
the similar footprint with their mother.
Feefee’s
footprint
BACK
NEXT
EXIT
1.
Which of the following is similar to the
above triangle?
A
B
C
BACK
NEXT
EXIT
Note: One triangle is a scale model of the
other triangle.
BACK
NEXT
EXIT
How do we know if two
triangles are similar or
proportional?
BACK
NEXT
EXIT
Triangles are similar (~)
if corresponding angles
are equal and the ratios
of the lengths of
corresponding sides are
equal.
BACK
NEXT
EXIT
Interior Angles of Triangles
B
A
C
The sum of the measure
of the angles of a
triangle is 1800.
C =1800
BACK
NEXT
EXIT
Determine whether the pair of triangles is similar.
Justify your answer.
Answer: Since the corresponding angles have equal
measures, the triangles are similar.
If the product of the
extremes equals the
product of the means
then a proportion
exists.
a c
=
b d
bc = ad
BACK
NEXT
EXIT
This tells us that  ABC and  XYZ are
similar and proportional.
AB
=K
XY
BC
=K
YZ
12
=2
6
8
=2
4
AC
=K
XZ
10
=2
5
BACK
NEXT
EXIT
Q: Can these triangles be similar?
BACK
NEXT
EXIT
Answer—Yes, right triangles can also
be similar but use the criteria.
AB
=
XY
AC
BC
=K
=
XZ
YZ
BACK
NEXT
EXIT
AB
=
XY
BC
=
YZ
AC
=K
XZ
6
8
10
=
=
=K
4
6
8
BACK
NEXT
EXIT
Do we have equality?
6
8
10
=
=
=K
4
6
8
6
8
= 1.5 but
= 1.3
4
6
This tells us our triangles are not
similar. You can’t have two different
scaling factors!
BACK
NEXT
EXIT
If we are given that two
triangles are similar or
proportional what can we
determine about the
triangles?
BACK
NEXT
EXIT
The two triangles below are known to
be similar, determine the missing value
X.
7.5 4.5
=
5
x
BACK
NEXT
EXIT
7.5 4.5
=
5
x
54.5 = 7.5x
22.5 = 7.5x
3= x
BACK
NEXT
EXIT
In the figure, the two triangles are similar.
What are c and d ?
A
5
P
10
c
B
R
4
d
Q
6
10 c
=
5 4
C
40 = 5c
8=c
BACK
NEXT
EXIT
In the figure, the two triangles are similar.
What are c and d ?
A
5
P
10
c
B
R
4
d
Q
6
C
10 6
=
30 = 10d
5 d
3=d
BACK
NEXT
EXIT
Sometimes we need to measure a distance
indirectly. A common method of indirect
measurement is the use of similar triangles.
17 6
=
102 h
36 = h
h
6
17
102
BACK
NEXT
EXIT
Click one of the buttons below
or press the enter key
BACK
NEXT
EXIT