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Building Triangles from Given Conditions

  • Grade 7
  • Mathematics
  • 7.G.A.2
  • Geometry
  • Free lesson

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 examples

Example 1

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.

Example 2

Can sides 6, 8, and 13 form a triangle? 6 + 8 = 14, which is greater than 13, so yes — exactly one triangle.

Example 3

Three given angles that sum to 180 make infinitely many triangles, all the same shape in different sizes. Three given sides make exactly one.

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 1: ¿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.

Ejemplo 2: ¿Pueden los lados 6, 8 y 13 formar un triángulo? 6 + 8 = 14, que es mayor que 13, así que sí — exactamente un triángulo.

Ejemplo 3: Tres ángulos dados que suman 180 forman infinitos triángulos, todos de la misma forma en distintos tamaños. Tres lados dados forman exactamente uno.

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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