The AA Similarity Criterion
Aligned to G-SRT.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
If two angles of one triangle equal two angles of another, the triangles are similar (AA). Because the angle sum is 180°, the third angles must also match, so all three angles agree. A dilation then scales one triangle onto the other, forcing proportional sides.
Worked example
Triangle ABC has angle A = 40°, angle B = 65°. Triangle DEF has angle D = 40°, angle E = 65°. Two angles match, so by AA the triangles are similar. Check the third angles: each equals 180 - 40 - 65 = 75°, confirming the match. Corresponding sides are therefore proportional.
Practice questions
- Triangle 1 has angles 50° and 60°. Triangle 2 has angles 60° and 70°. Are they similar by AA? Explain.
- Two right triangles each have an acute angle of 35°. Explain why they must be similar.
- In triangle ABC ~ triangle DEF by AA, if AB/DE = 3, what is BC/EF?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
El criterio de semejanza AA
Si dos ángulos de un triángulo son iguales a dos ángulos de otro, los triángulos son semejantes (AA). Como la suma de ángulos es 180°, los terceros ángulos también deben coincidir, así que los tres ángulos concuerdan. Una dilatación entonces escala un triángulo sobre el otro, forzando lados proporcionales.
Ejemplo: El triángulo ABC tiene ángulo A = 40°, ángulo B = 65°. El triángulo DEF tiene ángulo D = 40°, ángulo E = 65°. Dos ángulos coinciden, así que por AA los triángulos son semejantes. Verifica el tercer ángulo: cada uno mide 180 - 40 - 65 = 75°, confirmando la coincidencia. Por tanto los lados correspondientes son proporcionales.
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