Download Similar triangles

Similar Triangle

Problem 1:In the triangle ABC shown
below, A'C' is parallel to AC. Find the length
y of BC' and the length x of A'A.
Drill or pre-test
2.The picture below shows a right triangle. Find the length
of h; the height drawn to the hypotenuse.
Choose wisely
If two shapes are similar, one is an enlargement
of the other. This means that the two shapes
will have the same angles and their sides will be
in the same proportion (e.g. the sides of one
triangle will all be 3 times the sides of the other
etc.).
 Triangles ABC is similar to triangles XYZ written
as
ABC ~ XYZ, under the corresponding A<>X,B<->Y,
C<->Z, if and only if
i. All pair of corresponding angles are
congruent.
ii. All pair of corresponding sides are
proportional.


A
Consider the following figures:
B
Y
C
X
ABC ~
Z
XYZ if and only
We say that
if
Angles A is congruent to angle X ,
angle B is congruent to angle Y , angle
C is congruent to angle Z .
example
Given that ABC ~ DEF.
find the values of x and y.

B
3
E
4
A
View solution
X
C
D
8
F
Since the corresponding sides are
proportional, we have .
AB
BC
DE
EF
3
4
X
8
3
X
1
2
x=6;y =10
Solution
AC
DF
5
y
5
y
more information at
“yourteacher.com”

1. The triangles shown below are
similar. Find the exact values of a and
b shown on the picture
below.
Activity: # 1
2. Consider the picture shown below




(a) Use the Pythagorean Theorem to .nd
the value of a.
(b) Prove that the triangles ABE and
ACD are similar.
(c) Use similar triangles to .nd the value
of x.
(d) Find the value of b.
Activity:# 2
Problem 1. A person is standing 40 Ft.
away from a street light that is 30 Ft. tall.
How tall is he if his shadow
 is 10 Ft. long?

Assessment no.#1

Problem 2: A research team wishes to
determine the altitude of a mountain as
follows: They use a light source at L,
mounted on a structure of height 2 meters,
to shine a beam of light through the top of a
pole P' through the top of the mountain M'.
The height of the pole is 20 meters. The
distance between the altitude of the
mountain and the pole is 1000 meters. The
distance between the pole and the laser is 10
meters. We assume that the light source
mount, the pole and the altitude of the
mountain are in the same plane. Find the
altitude h of the mountain.
Assessment. #2
Assessment .#2
Answer keys
:
http://www.analyzemath.com/Geometry/simila
r_triangle_problems.html
http://www.mathopenref.com/similartriangles.
html
Reference
Reference
Solution no.#1 activity card
Solution no.#2 activity card