Track quiz
Eleven quick questions. Use the table if you get stuck.
| Idea | The rule |
|---|---|
| Three lines | They shut in a triangle, unless two are parallel or all meet at one spot. |
| By sides | Three match: equilateral. Exactly two: isosceles. None: scalene. |
| By angles | The widest corner names it. |
| The angle sum | The three corners add to 180°. |
| The missing angle | 180 minus the two you know. |
| The exterior angle | It equals the two far corners added. |
| Will it close | Each length is less than the other two added. |
| Longest, widest | They face each other. |
| Direct or roundabout | A road with a bend is longer than the direct road. So each side is shorter than the other two added. Checking the longest side is enough. A third side is longer than the difference of the other two. It is shorter than their sum. |
| Altitudes | An altitude is the perpendicular from a corner to the opposite side. Extend that side if it is needed. Its length is the height. Look at the two corners on that side. If either is obtuse, the foot falls outside. If either is 90°, the foot lands on that corner. If both are acute, it falls inside. In a right-angled triangle, two altitudes are the legs. |
| Two angles and a side | Take two angles at the ends of a side. A triangle exists when their sum is less than 180°. If the sum is 180° or more, it does not. The side length does not matter. The third angle is 180° minus their sum. |
Three lines are drawn, and every pair crosses. Must they shut in a triangle?
A triangle has sides of 34 mm, 55 mm and 34 mm. What is it called?
A triangle has corners of 85°, 60° and 35°. What is it called?
A triangle is redrawn four times as big. What happens to its three angles?
Two corners of a triangle are 33° and 84°. What is the third?
A triangle has corners of 38°, 67° and 75°. A side is carried past the 75° corner. What is the exterior angle?
Sticks of 4 cm, 4 cm and 9 cm are cut. Do they close into a triangle?
A triangle has corners of 30°, 50° and 100°. Which side is across from the 100° corner?
Sticks of 5 cm and 9 cm are given. Which third stick can close into a triangle?
A triangle has corners of 110°, 40° and 30°. Where does the altitude from the 40° corner land?
Two angles at the ends of a side are 72° and 98°. What is true?
Chapter 7 of Part I is A Tale of Three Intersecting Lines. Try its exercises to practise these ideas.
Next: Working with Fractions. Pieces that are not the same size. What happens when you add them.