Triangles

Grades 6–8 Geometry Triangles

Every triangle's three angles add to exactly 180°. That's the single most-used fact in geometry — cut any polygon into triangles and the rule keeps working.

Angles 70° and 60° — the third is: 180 − 70 − 60 = 50°

Naming triangles

By angles: acute (all < 90°), right (one 90°), obtuse (one > 90°)
By sides: equilateral (3 equal), isosceles (2 equal), scalene (none equal)

An equilateral triangle is also equiangular — every angle is exactly 60°.

The triangle inequality

Not every three sticks make a triangle. The two short sides must together be longer than the longest side — otherwise they can't reach each other. 3 + 4 > 5 ✓ but 2 + 3 = 5 gives a flat line, not a triangle.

Why engineers love triangles A triangle is the only rigid polygon — push on a square and it tilts into a rhombus, but a triangle can't deform without bending a side. That's why bridges, cranes, and roof trusses are triangles inside triangles.

Practice

Two angles are 40° and 60°. The third is ___°

Sides 4, 4, and 7 make a triangle that is:

Can sides 2, 3, and 6 form a triangle?

Each angle in an equilateral triangle is ___°

Next: quadrilaterals · Back: angles & lines

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