Geometric Construction — Drills
Geometric Construction 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 14 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Complement — Everything except the event. P(not A) = 1 - P(A).
- Vertex — A flat surface; a line where two faces meet; a corner point.
- Compass — Tools for drawing exact circles and lines — no measuring allowed.
- Complementary — Two angles summing to 90° / to 180°.
- Supplementary — Two angles summing to 90° / to 180°.
- Vertical angles — The opposite pair formed by two crossing lines — always equal.
- Base — The number being multiplied. In 53 the base is 5.
- Arc — Part of the edge; a "pizza slice" bounded by two radii.
- Transversal — A line that crosses two or more other lines.
- Co-interior angles — Between the parallels, same side. They add to 180°.
- Exterior angle — The angle formed by extending one side of a triangle.
- Parallel — Same slope, different intercept.
- Segment — Two endpoints and everything between them. Written AB.
- Limit — The value a function approaches as the input approaches some number.
Angles
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the complement of 29°.
Worked answer
61
90 - 29 = 61°
Problem 2
Find the complement of 45°.
Worked answer
45
90 - 45 = 45°
Triangle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A triangle has angles 51° and 70°. Find the third angle.
Worked answer
59
180 - 51 - 70 = 59°
Problem 2
A triangle has angles 66° and 50°. Find the third angle.
Worked answer
64
180 - 66 - 50 = 64°
Polygon
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find one interior angle of a regular 18-gon.
Worked answer
160
(18 - 2) × 180 = 2880°
2880 ÷ 18 = 160°
Problem 2
Find one interior angle of a regular pentagon.
Worked answer
108
(5 - 2) × 180 = 540°
540 ÷ 5 = 108°
Inequalities
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Can segments of length 11, 15 and 12 form a triangle?
- Yes
- No
Worked answer
Yes
Longest side: 15
The other two sum to 23
That is greater than 15, so a triangle exists.
Problem 2
Can segments of length 3, 6 and 1 form a triangle?
- Yes
- No
Worked answer
No
Longest side: 6
The other two sum to 4
That is not greater than 6, so no triangle exists.
Parallel lines
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two parallel lines are cut by a transversal. One angle is 56°. Find the alternate interior angle.
Worked answer
56
Alternate interior angles are equal, so 56°.
Problem 2
Two parallel lines are cut by a transversal. One angle is 71°. Find the alternate interior angle.
Worked answer
71
Alternate interior angles are equal, so 71°.
Construct
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
When bisecting an angle with a compass, why must the compass width stay the same for the two final arcs?
- So the crossing point is the same distance from both sides
- It does not actually matter
- So the drawing looks neat
- So the arcs fit on the page
Worked answer
So the crossing point is the same distance from both sides
Equal radii put the crossing point the same distance from each side of the angle.
A point equidistant from both sides lies exactly on the bisector — that is what makes it a proof.
Problem 2
Given only the three angle measures of a triangle, how many different triangles fit?
- Exactly two
- None
- Infinitely many
- Exactly one
Worked answer
Infinitely many
Angles fix the shape but not the size.
Every such triangle is similar to the others, at any scale you like.