CurriculumGrade 7Mathematics

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

  1. Can sides 6, 8, and 10 form a triangle? Show the check.
  2. Three angles measure 50°, 60°, and 70°. Do they form a triangle? How many?
  3. 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.

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En 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.

More Geometry lessons

Scale, Angles, Circles, and Volume7.G.B.4Scale Drawings7.G.A.1Cross Sections of Solids7.G.A.3Angle Relationships & Equations7.G.B.5Area, Volume & Surface Area7.G.B.6

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