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The Triangle & its Properties — Chapter Test

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Q1
The exterior angle of a triangle equals the sum of the two opposite ___ ?
Exterior angle = sum of the two opposite interior angles.
Q2
3, 4, 5 is a Pythagorean triple. So is 6, 8, ___ ?
6² + 8² = 36 + 64 = 100 = 10².
Q3
How many altitudes does a triangle have?
A triangle has 3 altitudes.
Q4
The angle sum of a triangle is ___ ?
The angle sum is 180°.
Q5
A right triangle has legs 3 and 4. What is the hypotenuse?
√(9 + 16) = 5.
Q6
A right triangle has legs 6 and 8. What is the hypotenuse?
√(36 + 64) = √100 = 10.
Q7
A right triangle has legs 5 and 12. What is the hypotenuse?
√(25 + 144) = √169 = 13.
Q8
Interior angles 50° and 60° give an exterior angle of ___ ?
50 + 60 = 110°.
Q9
An exterior angle is 120° and one opposite interior angle is 70°. The other is ___ ?
120 − 70 = 50°.
Q10
A median joins a vertex to the ___ of the opposite side.
A median joins a vertex to the midpoint of the opposite side.
Q11
A 5 m ladder leans on a wall with its base 3 m away. How high up the wall does it reach?
√(25 − 9) = √16 = 4 m (a 3-4-5 triangle).
Q12
Can sticks of 4 cm, 4 cm and 10 cm form a triangle?
4 + 4 = 8 is not greater than 10, so no.
Q13
A right triangle has hypotenuse 25 and one leg 7. What is the other leg?
√(625 − 49) = √576 = 24.
Q14
A right triangle has legs 9 and 12. What is the hypotenuse?
√(81 + 144) = √225 = 15.
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