◆ Tutorial

If It's True

Sometimes you want code to run only when a certain condition is met. Swift's if statement does exactly that.

Swift

let angle = 90

if angle == 90 {
    // this runs only when angle equals 90
    pen.turn(degrees: 90)
} else {
    // this runs for any other value
    pen.turn(degrees: Double(angle))
}

Swift's comparison operators:

Operators

a == b   // equal to
a != b   // not equal to
a <  b   // less than
a <= b   // less than or equal
a >  b   // greater than
a >= b   // greater than or equal

Conditions that evaluate to true or false are called Boolean expressions, named after mathematician George Boole.

📷 04-01-if-its-true.png Image coming soon

IM1 Curriculum Connection

Standard	Connection
Logic & Reasoning	Boolean expressions are the foundation of mathematical logic. A condition is either true or false — there's no middle ground — mirroring two-valued logic in proofs and set theory.

◆ Exercise

Classify an Angle

Write code that classifies an angle as acute, right, or obtuse based on its value in degrees. Print the result using print().

Acute: less than 90°
Right: exactly 90°
Obtuse: greater than 90° and less than 180°

Test your code with the values 45, 90, and 120.

📷 04-02-classify-an-angle.png Image coming soon

Solution

let angle = 45   // change this to test

if angle < 90 {
    print("Acute")
} else if angle == 90 {
    print("Right")
} else {
    print("Obtuse")
}

IM1 Curriculum Connection

Standard	Connection
Geometry — Angle Classification	Angles are classified by measure: acute (0°–90°), right (90°), obtuse (90°–180°), straight (180°), reflex (180°–360°). Identifying angle types is fundamental to geometry.

◆ Tutorial

Else If

When you have more than two possible outcomes, chain multiple conditions with else if.

Swift

let sides = 5

if sides == 3 {
    print("Triangle")
} else if sides == 4 {
    print("Quadrilateral")
} else if sides == 5 {
    print("Pentagon")
} else {
    print("Other polygon")
}

Swift evaluates each condition in order and executes the first block where the condition is true. Once a match is found, the remaining branches are skipped.

📷 04-03-else-if.png Image coming soon

IM1 Curriculum Connection

Standard	Connection
Geometry — Polygon Classification	Polygons are classified by number of sides: 3 = triangle, 4 = quadrilateral, 5 = pentagon, 6 = hexagon, etc. Each classification is a mutually exclusive category.

◆ Exercise

Triangle Classifier

Given three side lengths, classify the triangle as equilateral, isosceles, or scalene.

Equilateral: all three sides equal
Isosceles: exactly two sides equal
Scalene: all three sides different

Then also determine if it could be a right triangle using the Pythagorean theorem (a² + b² = c², where c is the longest side). Test with: (3, 4, 5), (5, 5, 5), (5, 5, 8).

📷 04-04-triangle-classifier.png Image coming soon

Solution

let a = 3, b = 4, c = 5   // change these to test

// Side classification
if a == b && b == c {
    print("Equilateral")
} else if a == b || b == c || a == c {
    print("Isosceles")
} else {
    print("Scalene")
}

// Right triangle check (sort sides first)
let sides = [a, b, c].sorted()
if sides[0]*sides[0] + sides[1]*sides[1] == sides[2]*sides[2] {
    print("Also a right triangle!")
}

IM1 Curriculum Connection

Standard	Connection
Geometry — Triangles	Triangle classification by sides: equilateral (all equal), isosceles (two equal), scalene (all different). The Pythagorean theorem a² + b² = c² identifies right triangles.

◆ Exercise

And & Or

Swift's logical operators let you combine conditions.

Operators

a && b   // AND: true only if both a and b are true
a || b   // OR:  true if at least one of a or b is true
!a       // NOT: inverts the truth value

Given an angle in degrees, use && and || to classify it as one of:

Zero angle (= 0°)
Acute (0° < angle < 90°)
Right (= 90°)
Obtuse (90° < angle < 180°)
Straight (= 180°)
Reflex (180° < angle < 360°)
Full rotation (= 360°)

📷 04-05-and-or.png Image coming soon

Solution

let angle = 135

if angle == 0 {
    print("Zero angle")
} else if angle > 0 && angle < 90 {
    print("Acute")
} else if angle == 90 {
    print("Right")
} else if angle > 90 && angle < 180 {
    print("Obtuse")
} else if angle == 180 {
    print("Straight")
} else if angle > 180 && angle < 360 {
    print("Reflex")
} else if angle == 360 {
    print("Full rotation")
}

IM1 Curriculum Connection

Standard	Connection
Geometry — Angles	Angles are classified across the full 0°–360° range. Compound inequalities (e.g. 90° < angle < 180°) represent intervals on the number line — a key IM1 concept.

◆ Exercise

Quadrilateral Checker

Given four side lengths and whether opposite sides are parallel (a Boolean), classify the shape.

Square: all sides equal, both pairs of opposite sides parallel
Rectangle: opposite sides equal, both pairs parallel
Rhombus: all sides equal, both pairs parallel, but not a square
Parallelogram: opposite sides equal and parallel
Trapezoid: exactly one pair of parallel sides
Irregular quadrilateral: none of the above

📷 04-06-quadrilateral-checker.png Image coming soon

Solution

// sides: top, right, bottom, left
let top = 80, right = 80, bottom = 80, left = 80
let horizontalParallel = true   // top ∥ bottom
let verticalParallel = true     // left ∥ right

let allEqual = top == right && right == bottom && bottom == left
let bothParallel = horizontalParallel && verticalParallel
let oppEqual = top == bottom && left == right

if allEqual && bothParallel {
    print("Square")
} else if oppEqual && bothParallel {
    print("Rectangle")
} else if allEqual && bothParallel {
    print("Rhombus")
} else if oppEqual {
    print("Parallelogram")
} else if horizontalParallel || verticalParallel {
    print("Trapezoid")
} else {
    print("Irregular quadrilateral")
}

IM1 Curriculum Connection

Standard	Connection
Geometry — Quadrilaterals	Quadrilaterals form a hierarchy: square ⊂ rectangle ⊂ parallelogram ⊂ quadrilateral. Boolean logic mirrors set inclusion — a square satisfies all conditions that a rectangle satisfies, plus more.

◆ Exercise

Right Angle Test

Given three angles of a triangle (in degrees), write a program that verifies they sum to 180°, checks for a right angle, and checks for equiangularity.

Verifies they sum to 180° (prints a warning if not)
Checks whether the triangle is right-angled (has a 90° angle)
Checks whether it is equiangular (all angles equal — which also means equilateral)

Test with: (90, 45, 45), (60, 60, 60), and (30, 60, 90).

📷 04-07-right-angle-test.png Image coming soon

Solution

let a1 = 90, a2 = 45, a3 = 45

if a1 + a2 + a3 != 180 {
    print("Warning: angles don't sum to 180°")
} else {
    if a1 == 90 || a2 == 90 || a3 == 90 {
        print("Right triangle")
    }
    if a1 == a2 && a2 == a3 {
        print("Equiangular (equilateral)")
    }
}

IM1 Curriculum Connection

Standard	Connection
Geometry — Triangle Angle Sum	The angle sum property of triangles states that the three interior angles always sum to 180°. An equiangular triangle has three 60° angles and must also be equilateral (equiangular ↔ equilateral for triangles).

◆ Exercise

Colour by Rule

Draw a row of 12 squares using a loop, and colour each square based on a rule: squares in positions divisible by 3 get one colour, positions divisible by 2 (but not 3) get another, and the rest get a third colour.

Hint: Swift's modulo operator % gives the remainder: i % 3 == 0 is true when i is divisible by 3.

📷 04-08-colour-by-rule.png Image coming soon

Solution

for i in 1...12 {
    if i % 3 == 0 {
        pen.fillColor = .blue
    } else if i % 2 == 0 {
        pen.fillColor = .yellow
    } else {
        pen.fillColor = .red
    }
    // Draw a filled square
    let square = Pen()
    for _ in 1...4 {
        square.addLine(distance: 50)
        square.turn(degrees: 90)
    }
    pen.addShape(pen: square)
    pen.move(distance: 60)
}

IM1 Curriculum Connection

Standard	Connection
Number — Divisibility	The modulo operator checks divisibility — a key number theory concept. Multiples of 3 and multiples of 2 create overlapping sets; the union and intersection can be described using Boolean logic.

◆ Exercise

Polygon Properties

Write a program that, given the number of sides and side length of a regular polygon, calculates and prints key properties, then draws the polygon.

The exterior angle (360° ÷ n)
The interior angle (180° − exterior)
The perimeter (n × side length)
Whether the polygon is convex (always true for regular polygons — print a note explaining why)

Then use a loop to draw the polygon at the calculated angles.

📷 04-09-polygon-properties.png Image coming soon

Solution

let n = 7              // heptagon
let sideLength = 80

let exteriorAngle = 360.0 / Double(n)
let interiorAngle = 180.0 - exteriorAngle
let perimeter = n * sideLength

print("Exterior angle: \(exteriorAngle)°")
print("Interior angle: \(interiorAngle)°")
print("Perimeter: \(perimeter)")
print("Regular polygons are always convex")
print("because all interior angles < 180°")

for _ in 1...n {
    pen.addLine(distance: Double(sideLength))
    pen.turn(degrees: exteriorAngle)
}

IM1 Curriculum Connection

Standard	Connection
Geometry — Regular Polygons	All interior angles of a regular polygon are equal to 180° − (360°/n). A polygon is convex when all interior angles are less than 180° — satisfied by all regular polygons.

Testing & Classifying

If It's True

Classify an Angle

Else If

Triangle Classifier

And & Or

Quadrilateral Checker

Right Angle Test

Colour by Rule

Polygon Properties