Loading Calculator...
Please wait a moment
Please wait a moment
Determine if two triangles are similar using AA, SAS, or SSS similarity theorems
Two triangles are similar if they have the same shape but not necessarily the same size. This means all corresponding angles are equal and all corresponding sides are proportional. There are three main methods to prove triangle similarity:
If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. The third angle must also be equal since angles sum to 180°.
If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, the triangles are similar.
If all three pairs of corresponding sides of two triangles are proportional, the triangles are similar.
The scale factor is the ratio of corresponding sides between similar triangles. If triangle B is similar to triangle A with scale factor k, then each side of B equals k times the corresponding side of A.
Congruent triangles are identical in both shape and size, while similar triangles have the same shape but can be different sizes. All congruent triangles are similar, but not all similar triangles are congruent.
Since the sum of angles in a triangle is always 180°, if two angles match, the third must also match. Having all three angles equal guarantees the triangles have the same shape, making them similar.
Divide any side of the larger triangle by the corresponding side of the smaller triangle. For example, if sides are 12 and 8, the scale factor is 12/8 = 1.5.
Yes, similar triangles can be rotated, reflected, or positioned differently. What matters is that corresponding angles are equal and corresponding sides are proportional, regardless of orientation.
Corresponding sides are sides that are in the same relative position in similar triangles. They're opposite equal angles. The shortest side corresponds to the shortest side, etc.
Similarity is used in scale models, maps, architectural plans, shadows for height measurement, and photo enlargement. Any time you scale something up or down proportionally, you're using similarity.
Similar triangles create proportions. If triangles are similar with sides a, b, c and a', b', c', then a/a' = b/b' = c/c'. These proportions can solve for unknown sides.
Yes! Once you know triangles are similar, you can use the scale factor or set up proportions to find missing side lengths or verify angle measurements.
Check if triangles are congruent using SSS, SAS, ASA, AAS, or HL
Find the scale factor between similar triangles
Calculate missing sides using proportions
Find angles in similar triangles
Calculate and apply scale factors