In Euclidean geometry, two triangles are known to be similar if two corresponding angles are congruent.^{[1]} Two angles are congruent if they have the same measure. This is called AA similarity. AA stands for angle, angle.
If ΔA is similar to ΔB, write "ΔA ∼ ΔB" and say, "Triangle A is similar to triangle B."
In Euclidean geometry the sum of the angles of a triangle is always 180° = 2π rad. This means that if two corresponding angles are congruent between two triangles, then the third angle must also be congruent. This is sometimes called AAA similarity for angle-angle-angle similarity. However, since AAA similarity is exactly the same thing as AA similarity, this term is rarely used.
In manipulative 1, angles A and A' are congruent and angles B and B' are congruent. Click on the blue points in manipulative 1 and drag them to change the figure.
Manipulative 1: Similar triangles by AA similarity |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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