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 remain the same size. 100º 30º 50º 100º 30º 50º

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

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

Harder example C A E D B 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 12 C B 9 3 x 3

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