Pythagorean Theorem — Drills
Pythagorean Theorem has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Base — The number being multiplied. In 53 the base is 5.
- Irrational — A real number that cannot be written as a fraction — its decimal never repeats and never ends.
- Leg — One of the two sides forming the right angle.
- Hypotenuse — The side opposite the right angle — always the longest.
- Diagonal — A segment joining two non-adjacent vertices.
- Height — The perpendicular distance from the base to the opposite corner.
Hyp
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A right triangle has legs 7 and 24. Find the hypotenuse.
Worked answer
25
72 + 242 = 49 + 576 = 625
c = √625 = 25
Problem 2
A right triangle has legs 6 and 8. Find the hypotenuse.
Worked answer
10
62 + 82 = 36 + 64 = 100
c = √100 = 10
Leg
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A right triangle has hypotenuse 25 and one leg 24. Find the other leg.
Worked answer
7
252 - 242 = 625 - 576 = 49
√49 = 7
Problem 2
A right triangle has hypotenuse 10 and one leg 8. Find the other leg.
Worked answer
6
102 - 82 = 100 - 64 = 36
√36 = 6
Parts of the whole
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
In a2 + b2 = c2, what do a and b represent?
- The hypotenuse and one leg
- The two legs
- The two angles
- Any two sides
Worked answer
The two legs
a and b are the legs — the sides forming the right angle. c is always the hypotenuse.
Problem 2
The Pythagorean theorem applies to which triangles?
- Right triangles only
- Equilateral triangles only
- All triangles
- Isosceles triangles only
Worked answer
Right triangles only
No right angle, no theorem. It fails for every other kind of triangle.
Converse
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Is a triangle with sides 9, 12 and 18 a right triangle?
- Yes
- No
Worked answer
No
92 + 122 = 225
182 = 324
Not equal, so it is not right-angled.
Problem 2
Is a triangle with sides 15, 20 and 25 a right triangle?
- Yes
- No
Worked answer
Yes
152 + 202 = 625
252 = 625
Equal, so it is right-angled.
Apply
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the distance between the points (6, 1) and (15, 13).
Worked answer
15
Horizontal gap: 9
Vertical gap: 12
81 + 144 = 225, so the distance is 15.
Problem 2
A 25 ft ladder reaches 20 ft up a wall. How far is its foot from the wall?
Worked answer
15
625 - 400 = 225
√225 = 15 ft