Unique Triangles
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?
IF THE ANSWER IS NO! THEN THE TRIANGLE IS SAID TO BE UNIQUE!
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.
Let’s Review
Resources All About Triangles Proving Congruence - shortcuts
Similar Triangles
Similar shapes Are Enlargements of each other Corresponding angles are equal Sides are related by the same scale factor
Similar Triangles Triangles are similar if matching angles 100º 30º 50º Triangles are similar if matching angles remain the same size. 100º 30º 50º
Show that these triangles are similar 10º 50º 120º 120º 10º 50º
To calculate a length x 3 x 3 15 5 1 3 5 4 6 15 12 18 Scale factor 3
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
Harder example A E D 3 4 9 6 C B 12 9 3 x 3
…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
…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 ?
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