State the Side-Side-Side (SSS) Similarity Theorem in your own words.

Two triangles are similar if the lengths of their corresponding sides are proportional.

If triangle PQR has sides PQ = 5, QR = 7, RP = 9 and triangle XYZ has sides XY = 10, YZ = 14, and ZX = 18, are the triangles similar? Explain why or why not.

Yes, the triangles are similar because the ratios of corresponding sides are equal (5/10 = 7/14 = 9/18 = 1/2).

Two triangles are similar if they have two pairs of corresponding sides that are proportional and the included angles are congruent.

Yes, the triangles are similar because AB/DE = AC/DF = 2/3, and angle A is congruent to angle D.

Two triangles are similar if they have two pairs of corresponding angles that are congruent.

I can prove that two triangles are similar using the AA, SAS, and SSS similarity theorems.

1
Side-Side-Side (SSS) similarity states that two triangles are similar if the lengths of their corresponding sides are proportional.
2
Side-Angle-Side (SAS) similarity states that two triangles are similar if they have two pairs of corresponding sides that are proportional and the included angles are congruent.
3
Angle-Angle (AA) similarity states that two triangles are similar if they have two pairs of corresponding angles that are congruent.