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

Prove that these triangles are similar : Type 1 Start by finding any angles which are given. A = D (given) C = F ( given) B = E ( 3rd angle in triangle) Triangles ABC are similar DEF

Prove that these triangles are similar : type 2 Find any given angles. C = F ( given) A =180 –( 30+80)=70 A = E (angles in a Δ add up to 180) B = G( 3rd angle in a triangle) Triangles ABC EGF are similar

Remember: You do not need to prove what the 3rd angle is Remember: You do not need to prove what the 3rd angle is. Important : The angles of the same triangle must be on the same side.

To calculate a length. Find PQ Let’s say that you have proven the triangles to be similar. Triangles ABC are similar PQR Open into ratios AB = BC = AC PQ QR PR Then decide on which one you do not need.

We do not need PR so that is the ratio we will not use. AB = BC Now put in values PQ QR 4 = 6 If the needed value is at the PQ 12 bottom, flip the fractions. PQ = 12 4 6 PQ = 4 x 12 = 8cm 6

Find side DE

Harder example: Proving similarity C A E D B A is common ADE = ABC ( corresponding angles) AED = ACB ( corresponding angles) Triangles ADE are similar ABC

…and then… AB & DE are parallel Explain why ABC is similar to CDE CED = BAC Alternate Angles A B EDC = ABC Alternate Angles ECD = ACB Vert Opp Angles D E Triangle ABC is similar to Triangle CDE