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<!DOCTYPE html>
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<div class="ch-label">Chapter 4 of 6</div>
<h1>Testing & Classifying</h1>
<p class="lead">Use conditionals and Boolean logic to classify shapes — triangles, quadrilaterals, and angles — by their properties.</p>
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<div class="banner-stat"><span class="stat-num">9</span><span class="stat-label">Sections</span></div>
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<div class="banner-stat"><span class="stat-num">7</span><span class="stat-label">Exercises</span></div>
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SECTION 01 — If It's True (Tutorial)
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<span class="section-tag tutorial">◆ Tutorial</span>
<h1>If It's True</h1>
<p class="lead">Sometimes you want code to run only when a certain condition is met. Swift's <strong>if statement</strong> does exactly that.</p>
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<pre><span class="kw">let</span> <span class="vr">angle</span> = <span class="num">90</span>
<span class="kw">if</span> <span class="vr">angle</span> == <span class="num">90</span> {
<span class="cm">// this runs only when angle equals 90</span>
pen.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
} <span class="kw">else</span> {
<span class="cm">// this runs for any other value</span>
pen.<span class="fn">turn</span>(degrees: <span class="tp">Double</span>(<span class="vr">angle</span>))
}</pre>
</div>
<p>Swift's comparison operators:</p>
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<pre><span class="vr">a</span> == <span class="vr">b</span> <span class="cm">// equal to</span>
<span class="vr">a</span> != <span class="vr">b</span> <span class="cm">// not equal to</span>
<span class="vr">a</span> < <span class="vr">b</span> <span class="cm">// less than</span>
<span class="vr">a</span> <= <span class="vr">b</span> <span class="cm">// less than or equal</span>
<span class="vr">a</span> > <span class="vr">b</span> <span class="cm">// greater than</span>
<span class="vr">a</span> >= <span class="vr">b</span> <span class="cm">// greater than or equal</span></pre>
</div>
<p>Conditions that evaluate to <code>true</code> or <code>false</code> are called <strong>Boolean expressions</strong>, named after mathematician George Boole.</p>
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<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Logic & Reasoning</td><td>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.</td></tr>
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</section>
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SECTION 02 — Classify an Angle
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<h1>Classify an Angle</h1>
<p class="lead">Write code that classifies an angle as <strong>acute</strong>, <strong>right</strong>, or <strong>obtuse</strong> based on its value in degrees. Print the result using <code>print()</code>.</p>
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<li>Acute: less than 90°</li>
<li>Right: exactly 90°</li>
<li>Obtuse: greater than 90° and less than 180°</li>
</ul>
<p>Test your code with the values 45, 90, and 120.</p>
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<pre><span class="kw">let</span> <span class="vr">angle</span> = <span class="num">45</span> <span class="cm">// change this to test</span>
<span class="kw">if</span> <span class="vr">angle</span> < <span class="num">90</span> {
<span class="fn">print</span>(<span class="str">"Acute"</span>)
} <span class="kw">else if</span> <span class="vr">angle</span> == <span class="num">90</span> {
<span class="fn">print</span>(<span class="str">"Right"</span>)
} <span class="kw">else</span> {
<span class="fn">print</span>(<span class="str">"Obtuse"</span>)
}</pre>
</div>
</div>
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<div class="im-table-header">IM1 Curriculum Connection</div>
<table class="im-table">
<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Geometry — Angle Classification</td><td>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.</td></tr>
</tbody>
</table>
</div>
</div>
</section>
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SECTION 03 — Else If (Tutorial)
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<h1>Else If</h1>
<p class="lead">When you have more than two possible outcomes, chain multiple conditions with <code>else if</code>.</p>
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<pre><span class="kw">let</span> <span class="vr">sides</span> = <span class="num">5</span>
<span class="kw">if</span> <span class="vr">sides</span> == <span class="num">3</span> {
<span class="fn">print</span>(<span class="str">"Triangle"</span>)
} <span class="kw">else if</span> <span class="vr">sides</span> == <span class="num">4</span> {
<span class="fn">print</span>(<span class="str">"Quadrilateral"</span>)
} <span class="kw">else if</span> <span class="vr">sides</span> == <span class="num">5</span> {
<span class="fn">print</span>(<span class="str">"Pentagon"</span>)
} <span class="kw">else</span> {
<span class="fn">print</span>(<span class="str">"Other polygon"</span>)
}</pre>
</div>
<p>Swift evaluates each condition in order and executes the first block where the condition is <code>true</code>. Once a match is found, the remaining branches are skipped.</p>
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<div class="im-table-wrap">
<div class="im-table-header">IM1 Curriculum Connection</div>
<table class="im-table">
<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Geometry — Polygon Classification</td><td>Polygons are classified by number of sides: 3 = triangle, 4 = quadrilateral, 5 = pentagon, 6 = hexagon, etc. Each classification is a mutually exclusive category.</td></tr>
</tbody>
</table>
</div>
</div>
</section>
<!-- ════════════════════════════════════════
SECTION 04 — Triangle Classifier
════════════════════════════════════════ -->
<section id="s04">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Triangle Classifier</h1>
<p class="lead">Given three side lengths, classify the triangle as <strong>equilateral</strong>, <strong>isosceles</strong>, or <strong>scalene</strong>.</p>
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<ul>
<li>Equilateral: all three sides equal</li>
<li>Isosceles: exactly two sides equal</li>
<li>Scalene: all three sides different</li>
</ul>
<p>Then also determine if it could be a <strong>right triangle</strong> using the Pythagorean theorem (a² + b² = c², where c is the longest side). Test with: (3, 4, 5), (5, 5, 5), (5, 5, 8).</p>
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<pre><span class="kw">let</span> <span class="vr">a</span> = <span class="num">3</span>, <span class="vr">b</span> = <span class="num">4</span>, <span class="vr">c</span> = <span class="num">5</span> <span class="cm">// change these to test</span>
<span class="cm">// Side classification</span>
<span class="kw">if</span> <span class="vr">a</span> == <span class="vr">b</span> && <span class="vr">b</span> == <span class="vr">c</span> {
<span class="fn">print</span>(<span class="str">"Equilateral"</span>)
} <span class="kw">else if</span> <span class="vr">a</span> == <span class="vr">b</span> || <span class="vr">b</span> == <span class="vr">c</span> || <span class="vr">a</span> == <span class="vr">c</span> {
<span class="fn">print</span>(<span class="str">"Isosceles"</span>)
} <span class="kw">else</span> {
<span class="fn">print</span>(<span class="str">"Scalene"</span>)
}
<span class="cm">// Right triangle check (sort sides first)</span>
<span class="kw">let</span> <span class="vr">sides</span> = [<span class="vr">a</span>, <span class="vr">b</span>, <span class="vr">c</span>].<span class="fn">sorted</span>()
<span class="kw">if</span> <span class="vr">sides</span>[<span class="num">0</span>]*<span class="vr">sides</span>[<span class="num">0</span>] + <span class="vr">sides</span>[<span class="num">1</span>]*<span class="vr">sides</span>[<span class="num">1</span>] == <span class="vr">sides</span>[<span class="num">2</span>]*<span class="vr">sides</span>[<span class="num">2</span>] {
<span class="fn">print</span>(<span class="str">"Also a right triangle!"</span>)
}</pre>
</div>
</div>
<div class="im-table-wrap">
<div class="im-table-header">IM1 Curriculum Connection</div>
<table class="im-table">
<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Geometry — Triangles</td><td>Triangle classification by sides: equilateral (all equal), isosceles (two equal), scalene (all different). The Pythagorean theorem a² + b² = c² identifies right triangles.</td></tr>
</tbody>
</table>
</div>
</div>
</section>
<!-- ════════════════════════════════════════
SECTION 05 — And & Or
════════════════════════════════════════ -->
<section id="s05">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>And & Or</h1>
<p class="lead">Swift's <strong>logical operators</strong> let you combine conditions.</p>
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<pre><span class="vr">a</span> && <span class="vr">b</span> <span class="cm">// AND: true only if both a and b are true</span>
<span class="vr">a</span> || <span class="vr">b</span> <span class="cm">// OR: true if at least one of a or b is true</span>
!<span class="vr">a</span> <span class="cm">// NOT: inverts the truth value</span></pre>
</div>
<p>Given an angle in degrees, use <code>&&</code> and <code>||</code> to classify it as one of:</p>
<ul>
<li>Zero angle (= 0°)</li>
<li>Acute (0° < angle < 90°)</li>
<li>Right (= 90°)</li>
<li>Obtuse (90° < angle < 180°)</li>
<li>Straight (= 180°)</li>
<li>Reflex (180° < angle < 360°)</li>
<li>Full rotation (= 360°)</li>
</ul>
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<pre><span class="kw">let</span> <span class="vr">angle</span> = <span class="num">135</span>
<span class="kw">if</span> <span class="vr">angle</span> == <span class="num">0</span> {
<span class="fn">print</span>(<span class="str">"Zero angle"</span>)
} <span class="kw">else if</span> <span class="vr">angle</span> > <span class="num">0</span> && <span class="vr">angle</span> < <span class="num">90</span> {
<span class="fn">print</span>(<span class="str">"Acute"</span>)
} <span class="kw">else if</span> <span class="vr">angle</span> == <span class="num">90</span> {
<span class="fn">print</span>(<span class="str">"Right"</span>)
} <span class="kw">else if</span> <span class="vr">angle</span> > <span class="num">90</span> && <span class="vr">angle</span> < <span class="num">180</span> {
<span class="fn">print</span>(<span class="str">"Obtuse"</span>)
} <span class="kw">else if</span> <span class="vr">angle</span> == <span class="num">180</span> {
<span class="fn">print</span>(<span class="str">"Straight"</span>)
} <span class="kw">else if</span> <span class="vr">angle</span> > <span class="num">180</span> && <span class="vr">angle</span> < <span class="num">360</span> {
<span class="fn">print</span>(<span class="str">"Reflex"</span>)
} <span class="kw">else if</span> <span class="vr">angle</span> == <span class="num">360</span> {
<span class="fn">print</span>(<span class="str">"Full rotation"</span>)
}</pre>
</div>
</div>
<div class="im-table-wrap">
<div class="im-table-header">IM1 Curriculum Connection</div>
<table class="im-table">
<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Geometry — Angles</td><td>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.</td></tr>
</tbody>
</table>
</div>
</div>
</section>
<!-- ════════════════════════════════════════
SECTION 06 — Quadrilateral Checker
════════════════════════════════════════ -->
<section id="s06">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Quadrilateral Checker</h1>
<p class="lead">Given four side lengths and whether opposite sides are parallel (a Boolean), classify the shape.</p>
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<ul>
<li><strong>Square</strong>: all sides equal, both pairs of opposite sides parallel</li>
<li><strong>Rectangle</strong>: opposite sides equal, both pairs parallel</li>
<li><strong>Rhombus</strong>: all sides equal, both pairs parallel, but not a square</li>
<li><strong>Parallelogram</strong>: opposite sides equal and parallel</li>
<li><strong>Trapezoid</strong>: exactly one pair of parallel sides</li>
<li><strong>Irregular quadrilateral</strong>: none of the above</li>
</ul>
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<pre><span class="cm">// sides: top, right, bottom, left</span>
<span class="kw">let</span> <span class="vr">top</span> = <span class="num">80</span>, <span class="vr">right</span> = <span class="num">80</span>, <span class="vr">bottom</span> = <span class="num">80</span>, <span class="vr">left</span> = <span class="num">80</span>
<span class="kw">let</span> <span class="vr">horizontalParallel</span> = <span class="kw">true</span> <span class="cm">// top ∥ bottom</span>
<span class="kw">let</span> <span class="vr">verticalParallel</span> = <span class="kw">true</span> <span class="cm">// left ∥ right</span>
<span class="kw">let</span> <span class="vr">allEqual</span> = <span class="vr">top</span> == <span class="vr">right</span> && <span class="vr">right</span> == <span class="vr">bottom</span> && <span class="vr">bottom</span> == <span class="vr">left</span>
<span class="kw">let</span> <span class="vr">bothParallel</span> = <span class="vr">horizontalParallel</span> && <span class="vr">verticalParallel</span>
<span class="kw">let</span> <span class="vr">oppEqual</span> = <span class="vr">top</span> == <span class="vr">bottom</span> && <span class="vr">left</span> == <span class="vr">right</span>
<span class="kw">if</span> <span class="vr">allEqual</span> && <span class="vr">bothParallel</span> {
<span class="fn">print</span>(<span class="str">"Square"</span>)
} <span class="kw">else if</span> <span class="vr">oppEqual</span> && <span class="vr">bothParallel</span> {
<span class="fn">print</span>(<span class="str">"Rectangle"</span>)
} <span class="kw">else if</span> <span class="vr">allEqual</span> && <span class="vr">bothParallel</span> {
<span class="fn">print</span>(<span class="str">"Rhombus"</span>)
} <span class="kw">else if</span> <span class="vr">oppEqual</span> {
<span class="fn">print</span>(<span class="str">"Parallelogram"</span>)
} <span class="kw">else if</span> <span class="vr">horizontalParallel</span> || <span class="vr">verticalParallel</span> {
<span class="fn">print</span>(<span class="str">"Trapezoid"</span>)
} <span class="kw">else</span> {
<span class="fn">print</span>(<span class="str">"Irregular quadrilateral"</span>)
}</pre>
</div>
</div>
<div class="im-table-wrap">
<div class="im-table-header">IM1 Curriculum Connection</div>
<table class="im-table">
<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Geometry — Quadrilaterals</td><td>Quadrilaterals form a hierarchy: square ⊂ rectangle ⊂ parallelogram ⊂ quadrilateral. Boolean logic mirrors set inclusion — a square satisfies all conditions that a rectangle satisfies, plus more.</td></tr>
</tbody>
</table>
</div>
</div>
</section>
<!-- ════════════════════════════════════════
SECTION 07 — Right Angle Test
════════════════════════════════════════ -->
<section id="s07">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Right Angle Test</h1>
<p class="lead">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.</p>
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<ol>
<li>Verifies they sum to 180° (prints a warning if not)</li>
<li>Checks whether the triangle is right-angled (has a 90° angle)</li>
<li>Checks whether it is equiangular (all angles equal — which also means equilateral)</li>
</ol>
<p>Test with: (90, 45, 45), (60, 60, 60), and (30, 60, 90).</p>
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<pre><span class="kw">let</span> <span class="vr">a1</span> = <span class="num">90</span>, <span class="vr">a2</span> = <span class="num">45</span>, <span class="vr">a3</span> = <span class="num">45</span>
<span class="kw">if</span> <span class="vr">a1</span> + <span class="vr">a2</span> + <span class="vr">a3</span> != <span class="num">180</span> {
<span class="fn">print</span>(<span class="str">"Warning: angles don't sum to 180°"</span>)
} <span class="kw">else</span> {
<span class="kw">if</span> <span class="vr">a1</span> == <span class="num">90</span> || <span class="vr">a2</span> == <span class="num">90</span> || <span class="vr">a3</span> == <span class="num">90</span> {
<span class="fn">print</span>(<span class="str">"Right triangle"</span>)
}
<span class="kw">if</span> <span class="vr">a1</span> == <span class="vr">a2</span> && <span class="vr">a2</span> == <span class="vr">a3</span> {
<span class="fn">print</span>(<span class="str">"Equiangular (equilateral)"</span>)
}
}</pre>
</div>
</div>
<div class="im-table-wrap">
<div class="im-table-header">IM1 Curriculum Connection</div>
<table class="im-table">
<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Geometry — Triangle Angle Sum</td><td>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).</td></tr>
</tbody>
</table>
</div>
</div>
</section>
<!-- ════════════════════════════════════════
SECTION 08 — Colour by Rule
════════════════════════════════════════ -->
<section id="s08">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Colour by Rule</h1>
<p class="lead">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.</p>
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<p><em>Hint: Swift's modulo operator <code>%</code> gives the remainder: <code>i % 3 == 0</code> is true when i is divisible by 3.</em></p>
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<pre><span class="kw">for</span> i <span class="kw">in</span> <span class="num">1</span>...<span class="num">12</span> {
<span class="kw">if</span> i % <span class="num">3</span> == <span class="num">0</span> {
pen.<span class="vr">fillColor</span> = .<span class="vr">blue</span>
} <span class="kw">else if</span> i % <span class="num">2</span> == <span class="num">0</span> {
pen.<span class="vr">fillColor</span> = .<span class="vr">yellow</span>
} <span class="kw">else</span> {
pen.<span class="vr">fillColor</span> = .<span class="vr">red</span>
}
<span class="cm">// Draw a filled square</span>
<span class="kw">let</span> <span class="vr">square</span> = <span class="tp">Pen</span>()
<span class="kw">for</span> _ <span class="kw">in</span> <span class="num">1</span>...<span class="num">4</span> {
<span class="vr">square</span>.<span class="fn">addLine</span>(distance: <span class="num">50</span>)
<span class="vr">square</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
}
pen.<span class="fn">addShape</span>(pen: <span class="vr">square</span>)
pen.<span class="fn">move</span>(distance: <span class="num">60</span>)
}</pre>
</div>
</div>
<div class="im-table-wrap">
<div class="im-table-header">IM1 Curriculum Connection</div>
<table class="im-table">
<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Number — Divisibility</td><td>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.</td></tr>
</tbody>
</table>
</div>
</div>
</section>
<!-- ════════════════════════════════════════
SECTION 09 — Polygon Properties
════════════════════════════════════════ -->
<section id="s09">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Polygon Properties</h1>
<p class="lead">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.</p>
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<ol>
<li>The exterior angle (360° ÷ n)</li>
<li>The interior angle (180° − exterior)</li>
<li>The perimeter (n × side length)</li>
<li>Whether the polygon is convex (always true for regular polygons — print a note explaining why)</li>
</ol>
<p>Then use a loop to draw the polygon at the calculated angles.</p>
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<pre><span class="kw">let</span> <span class="vr">n</span> = <span class="num">7</span> <span class="cm">// heptagon</span>
<span class="kw">let</span> <span class="vr">sideLength</span> = <span class="num">80</span>
<span class="kw">let</span> <span class="vr">exteriorAngle</span> = <span class="num">360.0</span> / <span class="tp">Double</span>(<span class="vr">n</span>)
<span class="kw">let</span> <span class="vr">interiorAngle</span> = <span class="num">180.0</span> - <span class="vr">exteriorAngle</span>
<span class="kw">let</span> <span class="vr">perimeter</span> = <span class="vr">n</span> * <span class="vr">sideLength</span>
<span class="fn">print</span>(<span class="str">"Exterior angle: \(exteriorAngle)°"</span>)
<span class="fn">print</span>(<span class="str">"Interior angle: \(interiorAngle)°"</span>)
<span class="fn">print</span>(<span class="str">"Perimeter: \(perimeter)"</span>)
<span class="fn">print</span>(<span class="str">"Regular polygons are always convex"</span>)
<span class="fn">print</span>(<span class="str">"because all interior angles < 180°"</span>)
<span class="kw">for</span> _ <span class="kw">in</span> <span class="num">1</span>...<span class="vr">n</span> {
pen.<span class="fn">addLine</span>(distance: <span class="tp">Double</span>(<span class="vr">sideLength</span>))
pen.<span class="fn">turn</span>(degrees: <span class="vr">exteriorAngle</span>)
}</pre>
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</div>
<div class="im-table-wrap">
<div class="im-table-header">IM1 Curriculum Connection</div>
<table class="im-table">
<thead><tr><th>Standard</th><th>Connection</th></tr></thead>
<tbody>
<tr><td>Geometry — Regular Polygons</td><td>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.</td></tr>
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