Quadrilaterals & Polygon Properties — Drills
Quadrilaterals & Polygon Properties has 9 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 13 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Mean — Two kinds of centre: the balance point, and the middle value.
- Bisect — Cut exactly in half.
- Supplementary — Two angles summing to 90° / to 180°.
- Base — The number being multiplied. In 53 the base is 5.
- Congruent — Same size and same shape. Written △ ABC ≅ △ DEF.
- Exterior angle — The angle formed by extending one side of a triangle.
- Perpendicular — Slopes multiply to -1 — negative reciprocals.
- Polygon — A closed figure made of straight segments that meet only at endpoints.
- Regular polygon — All sides equal and all angles equal.
- Parallelogram — A quadrilateral with both pairs of opposite sides parallel.
- Rhombus — A parallelogram with four congruent sides.
- Trapezoid — A quadrilateral with exactly one pair of parallel sides.
- Diagonal — A segment joining two non-adjacent vertices.
Anglesum
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the sum of the interior angles of a octagon.
Worked answer
1080
n = 8, so 8 - 2 = 6 triangles
6 × 180 = 1080°
Problem 2
Find the sum of the interior angles of a decagon.
Worked answer
1440
n = 10, so 10 - 2 = 8 triangles
8 × 180 = 1440°
Exterior
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the sum of the exterior angles of any convex polygon.
Worked answer
360
You turn through one full circle.
360°, whatever n is.
Regular
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find each interior angle of a regular 20-gon.
Worked answer
162
Exterior: 360 ÷ 20 = 18
Interior: 180 - 18 = 162°
Problem 2
Find each exterior angle of a regular 5-gon.
Worked answer
72
360 ÷ 5 = 72°
Family
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Is every square a rectangle?
- Yes
- Only in coordinate geometry
- No
- Only sometimes
Worked answer
Yes
Check whether the first shape meets every condition of the second.
Answer: Yes.
Problem 2
Is every rectangle a square?
- Only in coordinate geometry
- Only sometimes
- No
- Yes
Worked answer
No
Check whether the first shape meets every condition of the second.
Answer: No.
Parallelogram
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
In parallelogram ABCD, m∠ A = 132°. Find m∠ C.
Worked answer
132
∠ A and ∠ C are opposite, so congruent.
132°
Problem 2
In parallelogram ABCD, m∠ A = 32°. Find m∠ C.
Worked answer
32
∠ A and ∠ C are opposite, so congruent.
32°
Diagonals
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A quadrilateral with congruent diagonals that bisect each other is a
- rectangle
- kite
- rhombus
- trapezoid
Worked answer
rectangle
Work through the diagonal properties one at a time.
That gives a rectangle.
Problem 2
A quadrilateral with perpendicular diagonals that bisect each other is a
- trapezoid
- kite
- rhombus
- rectangle
Worked answer
rhombus
Work through the diagonal properties one at a time.
That gives a rhombus.
Midsegment
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A trapezoid has bases 18 and 28. Find its midsegment.
Worked answer
23
18 + 282 = 23
Problem 2
A trapezoid has one base 5 and midsegment 9. Find the other base.
Worked answer
13
5 + x2 = 9
5 + x = 18
x = 13
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
In parallelogram ABCD, m∠ A = (5x + 7)° and m∠ C = (9x - 73)°. Find x.
Worked answer
20
5x + 7 = 9x - 73
80 = 4x
x = 20
Both angles are 107° ✓
Problem 2
In parallelogram ABCD, m∠ A = (4x + 35)° and m∠ C = (7x - 40)°. Find x.
Worked answer
25
4x + 35 = 7x - 40
75 = 3x
x = 25
Both angles are 135° ✓
Identifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A quadrilateral has diagonals that bisect each other, are congruent and perpendicular. Name it.
Worked answer
square
Bisecting each other makes it a parallelogram.
Congruent means rectangle; perpendicular means rhombus; both means square.
So: a square.
Problem 2
A quadrilateral has diagonals that bisect each other but are neither congruent nor perpendicular. Name it.
Worked answer
parallelogram
Bisecting each other makes it a parallelogram.
Congruent means rectangle; perpendicular means rhombus; both means square.
So: a parallelogram.