Download 7.1 - Congruence and Similarity in Triangles

Congruent Triangles
When 2 triangles are congruent, they will have exactly the same
three sides and exactly the same three angles.
The small, blue triangle is made
using the middle of each side of the
large, black triangle.
Are the four small triangles
congruent?
Are there similar triangles in this
design?
Yes, all the small triangles are similar
to the large, black one.
Create a triangle that is similar but not congruent to ∆𝐴𝐵𝐶.
SIMILAR: same angles
CONGRUENT: same angles and sides
So our triangle must have the same
angles as ∆𝑨𝑩𝑪 but different sides.
A
3.3 cm
A
60o
6.6 cm
B
4.8 cm
60o
C
7.4 cm
B
2.4 cm
C
3.7 cm
Is ∆𝐷𝐸𝐹 similar to ∆𝐴𝐵𝐶?
A
3.3 cm
D
B
2.4 cm
1.2 cm
F
60o
1.5 cm
60o
3.7 cm
C
E
The sides are not proportional, so the triangles are not similar.
D
6.0 cm
3.6 cm
C
E
8.0 cm
y
B
x
A
To find x, set up a proportion:
𝐴𝐵 𝐵𝐷
=
𝐸𝐶 𝐶𝐷
Show that the two triangles in this
diagram are similar. Then
determine the values of x and y.
Angle BAD = Angle CED
Angle ABD = Angle ECD
So, ∆ABD ~ ∆ECD (they are similar)
To find y, set up a proportion:
𝐴𝐷 𝐵𝐷
=
𝐸𝐷 𝐶𝐷
𝑥
14.0
=
6.0
6.0
𝑦 + 3.6 14.0
=
3.6
6.0
14.0
𝑥 = 6.0
6.0
14.0
𝑦 = 3.6
− 3.6
6.0
𝒙 = 𝟏𝟒. 𝟎
𝒚 = 𝟒. 𝟖
If two triangles are congruent, then they are also
similar
If two triangles are similar, they are not always
congruent
If two pairs of corresponding angles in two triangles
are equal, then the triangles are similar
If in addition two corresponding sides are equal,
then the triangles are congruent