Transcript Unique and Similar Triangles

Unique Triangles are triangles that do not have an equivalent.
This means there is not another triangle that has the exact
dimensions or shape.
What are the facts or conditions that you need to know to create a
unique triangle?
In other words, if two people had the same information is it
possible for them to construct two different triangles?
THEN THE TRIANGLE IS SAID TO BE UNIQUE!
ASA
two angles must sum to less than 180º
SSS
AAS
two angles must sum to less than 180º
SAS
two shortest sides are longer than the third side
Any set of data that fits these conditions will result in one unique triangle.
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All About Triangles
Proving Congruence - shortcuts
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Are Enlargements of each other
Corresponding angles are equal
Sides are related by the same scale factor
100º
30º
50º
Triangles are similar
if matching angles
remain the same size.
100º
30º
50º
10º
50º
120º
10º
50º
120º
5
15
5
x3
4
x3
6
Scale factor 3
15
1
3
18
Scale factor 1/3
12
A
3
4
D
E
6
C
B
Triangle ABC is similar to triangle ADE.
DE is parallel to BC.
Calculate the length of BC
A
3
D
4
9
E
6
C
B
12
9
3
x3
AB & DE are parallel
Explain why ABC is similar to CDE
5
A
B
<CED = <BAC Alternate Angles
3
<EDC = <ABC Alternate Angles
C
6
<ECD = <ACB Vert Opp Angles
E
D
?
Triangle ABC is similar to Triangle CDE
Calculate the length of DE
AC corresponds to CE
Scale Factor = 2
5
A
B
AB corresponds to DE
DE = 2 x AB
3
C
DE = 10cm
6
E
D
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To calculate missing sides, we first of all need
the scale factor
We then either multiply or divide by the scale
factor
To show that 2 shapes are similar we can either:
 show that all of the sides are connected by the scale
factor
 or show that matching angles are the same