Building Triangles from Given Conditions
Aligned to 7.G.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Given side lengths or angles, sometimes exactly one triangle can be built, sometimes many, sometimes none. Three sides form a triangle only if each side is shorter than the sum of the other two. Three angles that add to 180° give many similar triangles.
Worked example
Can sides 4, 5, and 12 form a triangle? Check the longest side: 4 + 5 = 9, and 9 < 12. Since the two shorter sides do not reach across, no triangle is possible.
Practice questions
- Can sides 6, 8, and 10 form a triangle? Show the check.
- Three angles measure 50°, 60°, and 70°. Do they form a triangle? How many?
- Two angles of a triangle are 40° and 65°. Find the third angle.
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
Construir Triángulos con Condiciones Dadas
Con longitudes de lados o ángulos dados, a veces se forma exactamente un triángulo, a veces muchos y a veces ninguno. Tres lados forman un triángulo solo si cada lado es menor que la suma de los otros dos. Tres ángulos que suman 180° dan muchos triángulos semejantes.
Ejemplo: ¿Pueden los lados 4, 5 y 12 formar un triángulo? Revisa el lado más largo: 4 + 5 = 9, y 9 < 12. Como los dos lados cortos no alcanzan a cerrarse, no se puede formar un triángulo.
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