Transcript Solving for the unknown in Similar Triangles

Solving for the unknown in Similar
Triangles
Using Scale factor
Scale factor works too!
 Remember that scale factor is a constant factor by which we
can multiply in order to either reduce or enlarge an object.
 In similar triangles, one way to solve for the missing
information was to set up a proportion and solve for x
 Scale factor can also be used to solve for missing sides.
 Let’s compare the two methods, using the same problem.
Using a Proportion:
 Let’s say we have similar triangles. We have to solve for a missing
side. We can set up a proportion to solve for x and find the
solution!
3.2
=
x
4.6
6.2
With cross multiplication, we find the solution.
≈ 4.3
Using Scale Factor:
3.2
x
4.6
6.2
 We can also use scale factor to solve for x.
 If we know that 6.2 ÷ 4.6 = 1.347826
then we can use this factor to calculate the unknown side:
3.2 (1.347826) = 4.3130432 ≈ 4.3
When a proportion may be best:
 The one time that it may be best to use a
proportion to solve is when you a situation where
a section of one of the sides is unknown:
X
9.2
3.4
5.5
Let’s say that you are helping
to set up the official Christmas
tree at City Hall. You have a
5.5 meter ladder that is leaning
against the tree, and it reaches
3.4 meters up the tree.
You know that the blue cable
holding the tree in place is 9.2
meters long, and it is at the
exact same angle as the
ladder.
How tall is the tree?
 Using proportion to set it up, we can have the
following problem to solve:
=
5.5 (3.4 + x) = 3.4(9.2)
18.7 + 5.5 x = 31.28
5.5 x = 12.58
x = 12.58 ÷ 5.5
x = 2.2872727
x ≈ 2.3 meters
The height of the tree is 3.4 + x , so 3.4 + 2.3 = 5.7 meters
Why setting up a proportion can help
this year:
 Further in our studies this year, we will be working on
solving algebraic equations.
 When you know how to set up proportions and solve, that
method is most like the process used to solve for the
unknown in algebraic equations.
 What I recommend: be capable of solving similar triangle
problems with both scale factor and with proportions.
 But for getting ready for algebraic equations, I suggest you
use the proportion method.