A Tale of Three Intersecting Lines

Which side lengths make a triangle, the angle sum of a triangle, exterior angles, and the kinds of triangle.

Key ideas

Triangle inequality: the two shorter sides must add up to more than the longest side.
The angles of a triangle add up to 180°.
An exterior angle equals the sum of the two interior opposite angles.
By sides: equilateral (all equal), isosceles (two equal), scalene (none equal).
By angles: acute (all less than 90°), right (one 90°), obtuse (one more than 90°).
In an isosceles triangle, the angles opposite the equal sides are equal.

Angle sum	∠A + ∠B + ∠C = 180°
Exterior angle	exterior angle = sum of the two interior opposite angles
Equilateral triangle	each angle = 60°

Allowing sides where the shorter two exactly equal the longest (they make a flat line, not a triangle).
Adding all three interior angles to get an exterior angle.
Thinking a triangle can have two right angles.

Which of these can be the sides of a triangle? (i) 10, 6, 20 (ii) 9, 10, 19 (iii) 11, 5, 16 (all in cm)

Working: check that the two shorter sides add up to more than the longest

Answer: (i) no, (ii) no, (iii) no