Angle Relationships
Aligned to 8.G.A.5 — Common Core State Standards for Mathematics.
What this lesson teaches
The interior angles of a triangle sum to 180°. When parallel lines are cut by a transversal, alternate interior angles are equal and corresponding angles are equal. Two triangles with two pairs of equal angles (AA) are similar.
Worked example
A triangle has angles 50° and 60°, so the third angle is 180° − 50° − 60° = 70°. If a second triangle also has angles 50° and 60°, then by the angle-angle (AA) criterion the two triangles are similar.
Practice questions
- Two angles of a triangle are 45° and 85°. Find the third.
- Parallel lines are cut by a transversal and one angle is 110°. Find its alternate interior angle.
- Explain why two triangles that each have angles of 30° and 70° must be similar.
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
Relaciones entre Ángulos
Los ángulos interiores de un triángulo suman 180°. Cuando rectas paralelas son cortadas por una transversal, los ángulos alternos internos son iguales y los ángulos correspondientes son iguales. Dos triángulos con dos pares de ángulos iguales (AA) son semejantes.
Ejemplo: Un triángulo tiene ángulos de 50° y 60°, así que el tercer ángulo es 180° − 50° − 60° = 70°. Si un segundo triángulo también tiene ángulos de 50° y 60°, entonces por el criterio ángulo-ángulo (AA) los dos triángulos son semejantes.
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