Definitions, Postulates & Reasoning — Drills
Definitions, Postulates & Reasoning has 6 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 9 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Bisect — Cut exactly in half.
- Congruent — Same size and same shape. Written △ ABC ≅ △ DEF.
- Midpoint — The point halfway between two others: average the x values and average the y values.
- Undefined term — Point, line and plane. Described but never defined, because any definition would use them.
- Postulate — A statement accepted without proof, such as "two points determine exactly one line."
- Segment — Two endpoints and everything between them. Written AB.
- Ray — One endpoint and everything beyond it in one direction. Written AB.
- Counterexample — A single case that makes a claim false. One is enough.
- Number line — A line with numbers increasing to the right.
Notation
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which symbol means the ray through A and B?
Worked answer
\overrightarrow{AB}
A ray is written AB
Because it starts at A and carries on past B.
Problem 2
Which symbol means the line through A and B?
Worked answer
\overleftrightarrow{AB}
A line is written ↔AB
Because it runs forever in both directions.
Segadd
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
B is between A and C. AC = 24 and AB = 7. Find BC.
Worked answer
17
AB + BC = AC
BC = 24 - 7 = 17
Problem 2
B is between A and C. AB = 13 and BC = 14. Find AC.
Worked answer
27
AB + BC = AC
13 + 14 = 27
Midpoint
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
M is the midpoint of PQ and PM = 17. Find PQ.
Worked answer
34
MQ = PM = 17
PQ = 17 + 17 = 34
Problem 2
M is the midpoint of PQ and PM = 24. Find PQ.
Worked answer
48
MQ = PM = 24
PQ = 24 + 24 = 48
Bisector
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
OB bisects ∠ AOC. If m∠ AOB = 42°, find m∠ AOC.
Worked answer
84
m∠ AOC = 2 × 42
= 84°
Problem 2
OB bisects ∠ AOC. If m∠ AOB = 56°, find m∠ AOC.
Worked answer
112
m∠ AOC = 2 × 56
= 112°
Angadd
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
OB is inside ∠ AOC. m∠ AOB = 26° and m∠ AOC = 82°. Find m∠ BOC.
Worked answer
56
26 + m∠ BOC = 82
m∠ BOC = 56°
Problem 2
OB is inside ∠ AOC. m∠ AOB = 39° and m∠ AOC = 85°. Find m∠ BOC.
Worked answer
46
39 + m∠ BOC = 85
m∠ BOC = 46°
Terms
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which of these is an undefined term in geometry?
- Segment
- Line
- Midpoint
- Angle
Worked answer
Line
Point, line and plane are taken as undefined.
Everything else is defined using them.