1. Similar Triangles

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

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

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

5. 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

6. 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

7. 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.

8. 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.

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

10. Find side DE

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

13. …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