1. Unique Triangles

2. Unique 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?

3. IF THE ANSWER IS NO!
THEN THE TRIANGLE IS SAID TO BE UNIQUE!

5. Conditions for Unique Triangles
AAS
ASA
two angles must sum to less than 180º
two angles must sum to less than 180º
SSS
SAS
two shortest sides are longer than the third side
Any set of data that fits these conditions will result in one unique triangle.

6. Let’s Review

7. Resources
All About Triangles
Proving Congruence - shortcuts

8. Similar Triangles

9. Similar shapes Are Enlargements of each other
Corresponding angles are equal
Sides are related by the same scale factor

10. Similar Triangles Triangles are similar if matching angles
100º
30º
50º
Triangles are similar
if matching angles
remain the same size.
100º
30º
50º

11. Show that these triangles are similar
10º
50º
120º
120º
10º
50º

12. To calculate a length x 3 x 3 15 5 1 3 5 4 6 15 12 18 Scale factor 3

13. Harder example Triangle ABC is similar to triangle ADE.3 4 6
Triangle ABC is similar to triangle ADE.
DE is parallel to BC.
Calculate the length of BC

14. Harder example A E D 3 4 9 6 C B 12 9 3
x 3

15. …and then… Triangle ABC is similar to Triangle CDE
AB & DE are parallel
Explain why ABC is similar to CDE 5 A B
<CED = <BAC Alternate Angles 3
<EDC = <ABC Alternate Angles C
<ECD = <ACB Vert Opp Angles 6 D E ?
Triangle ABC is similar to Triangle CDE

16. …and then… 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 D E ?

17. Summary – Similar Shapes
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