Two or more triangles are similar if they have the same shape but can be different sizes.
How can we know if two triangles are similar?
We can know if triangles are similar if they can satisfy any one of the following conditions:
AAA (angle-angle-angle)
All three pairs of corresponding angles are the same.
The Corresponding pairs of angles are:
∠ACB = ∠PQR
∠ABC = ∠PRQ
∠CAB = ∠QPR
Therefore, these triangles are similar.
SSS (side-side-side)
All three sides in one triangle are in the same proportion to the corresponding sides in the other.
In the above triangles, the corresponding pairs of sides are:
(AC & PQ)
(CB & QR)
(AB & PR)
AC is half of PQ
CB is half of QR
AB is half of PR
All three corresponding pairs of sides are in the same proportion. Hence, the two triangles are similar.
SAS (side-angle-side)
Two corresponding pairs of sides are in the same proportion and the included corresponding angles are equal.
In the above triangles, the two corresponding pairs of sides are:
(AC & PQ)
(AB & PR)
The corresponding angles (∠CAB and ∠QPR) are equal.
AC is half of PQ
AB is half of PR
∠CAB = ∠QPR
Two corresponding pairs of sides are in the same proportion and the included angle is equal. Hence, the two triangles are similar.
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