716 lines
29 KiB
TypeScript
716 lines
29 KiB
TypeScript
import React, { useRef, useState, useEffect } from "react";
|
||
import {
|
||
ArrowDown,
|
||
Check,
|
||
Target,
|
||
Layers,
|
||
Calculator,
|
||
BookOpen,
|
||
} from "lucide-react";
|
||
import InteractiveTransversal from "../../../components/lessons/InteractiveTransversal";
|
||
import InteractiveTriangle from "../../../components/lessons/InteractiveTriangle";
|
||
import PolygonWidget from "../../../components/lessons/PolygonWidget";
|
||
import Quiz from "../../../components/lessons/Quiz";
|
||
import { ANGLES_QUIZ_DATA } from "../../../utils/constants";
|
||
import { Frac } from "../../../components/Math";
|
||
|
||
interface LessonProps {
|
||
onFinish?: () => void;
|
||
}
|
||
|
||
const LinesAnglesLesson: React.FC<LessonProps> = ({ onFinish }) => {
|
||
const [activeSection, setActiveSection] = useState(0);
|
||
const sectionsRef = useRef<(HTMLElement | null)[]>([]);
|
||
|
||
const scrollToSection = (index: number) => {
|
||
setActiveSection(index);
|
||
sectionsRef.current[index]?.scrollIntoView({
|
||
behavior: "smooth",
|
||
block: "start",
|
||
});
|
||
};
|
||
|
||
useEffect(() => {
|
||
const observer = new IntersectionObserver(
|
||
(entries) => {
|
||
entries.forEach((entry) => {
|
||
if (entry.isIntersecting) {
|
||
const index = sectionsRef.current.indexOf(
|
||
entry.target as HTMLElement,
|
||
);
|
||
if (index !== -1) setActiveSection(index);
|
||
}
|
||
});
|
||
},
|
||
{ rootMargin: "-20% 0px -60% 0px" },
|
||
);
|
||
sectionsRef.current.forEach((section) => {
|
||
if (section) observer.observe(section);
|
||
});
|
||
return () => observer.disconnect();
|
||
}, []);
|
||
|
||
const SectionMarker = ({
|
||
index,
|
||
title,
|
||
icon: Icon,
|
||
}: {
|
||
index: number;
|
||
title: string;
|
||
icon: any;
|
||
}) => {
|
||
const isActive = activeSection === index;
|
||
const isPast = activeSection > index;
|
||
return (
|
||
<button
|
||
onClick={() => scrollToSection(index)}
|
||
className={`flex items-center gap-3 p-3 w-full rounded-lg transition-all ${isActive ? "bg-white shadow-md border border-emerald-100" : "hover:bg-slate-100"}`}
|
||
>
|
||
<div
|
||
className={`w-8 h-8 rounded-full flex items-center justify-center shrink-0 ${isActive ? "bg-emerald-600 text-white" : isPast ? "bg-emerald-400 text-white" : "bg-slate-200 text-slate-500"}`}
|
||
>
|
||
{isPast ? (
|
||
<Check className="w-4 h-4" />
|
||
) : (
|
||
<Icon className="w-4 h-4" />
|
||
)}
|
||
</div>
|
||
<div className="text-left">
|
||
<p
|
||
className={`text-sm font-bold ${isActive ? "text-emerald-900" : "text-slate-600"}`}
|
||
>
|
||
{title}
|
||
</p>
|
||
</div>
|
||
</button>
|
||
);
|
||
};
|
||
|
||
return (
|
||
<div className="flex flex-col lg:flex-row min-h-screen">
|
||
<aside className="w-full lg:w-64 lg:fixed lg:top-20 lg:bottom-0 lg:overflow-y-auto p-4 border-r border-slate-200 bg-slate-50 lg:bg-transparent z-0 hidden lg:block">
|
||
<nav className="space-y-2">
|
||
<SectionMarker index={0} title="Parallel Lines" icon={Target} />
|
||
<SectionMarker index={1} title="Triangles" icon={Layers} />
|
||
<SectionMarker
|
||
index={2}
|
||
title="Special Triangles"
|
||
icon={Calculator}
|
||
/>
|
||
<SectionMarker index={3} title="Polygons" icon={Calculator} />
|
||
<SectionMarker index={4} title="Practice" icon={BookOpen} />
|
||
</nav>
|
||
</aside>
|
||
|
||
<div className="flex-1 lg:ml-64 p-6 md:p-12 max-w-4xl mx-auto">
|
||
{/* Section 1: Parallel Lines */}
|
||
<section
|
||
ref={(el) => {
|
||
sectionsRef.current[0] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center mb-24 pt-20 lg:pt-0"
|
||
>
|
||
<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
|
||
Parallel Lines & Transversals
|
||
</h2>
|
||
<div className="prose prose-slate text-lg text-slate-600 mb-8">
|
||
<p>
|
||
When two parallel lines are cut by a transversal, 8 angles are
|
||
formed. They fall into exactly two groups:{" "}
|
||
<strong>equal angles</strong> and{" "}
|
||
<strong>supplementary pairs</strong> (summing to 180°). Know one
|
||
angle → find all eight.
|
||
</p>
|
||
</div>
|
||
|
||
<div className="bg-emerald-50 border border-emerald-200 rounded-2xl p-6 mb-8 space-y-5">
|
||
<h3 className="text-lg font-bold text-emerald-900">
|
||
The 5 Angle-Pair Relationships
|
||
</h3>
|
||
|
||
<div className="overflow-x-auto rounded-xl border border-emerald-200">
|
||
<table className="w-full text-sm border-collapse">
|
||
<thead>
|
||
<tr className="bg-emerald-900 text-white">
|
||
<th className="p-3 text-left">Angle Pair</th>
|
||
<th className="p-3 text-left">Location</th>
|
||
<th className="p-3 text-left">Relationship</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody className="divide-y divide-emerald-100">
|
||
<tr className="bg-emerald-50">
|
||
<td className="p-3 font-bold text-emerald-800">
|
||
Corresponding
|
||
</td>
|
||
<td className="p-3">
|
||
Same side, same position at each intersection
|
||
</td>
|
||
<td className="p-3 font-bold text-emerald-700">Equal</td>
|
||
</tr>
|
||
<tr className="bg-white">
|
||
<td className="p-3 font-bold text-emerald-800">
|
||
Alternate Interior
|
||
</td>
|
||
<td className="p-3">
|
||
Between the parallel lines, opposite sides
|
||
</td>
|
||
<td className="p-3 font-bold text-emerald-700">Equal</td>
|
||
</tr>
|
||
<tr className="bg-emerald-50">
|
||
<td className="p-3 font-bold text-emerald-800">
|
||
Alternate Exterior
|
||
</td>
|
||
<td className="p-3">
|
||
Outside the parallel lines, opposite sides
|
||
</td>
|
||
<td className="p-3 font-bold text-emerald-700">Equal</td>
|
||
</tr>
|
||
<tr className="bg-white">
|
||
<td className="p-3 font-bold text-slate-600">
|
||
Co-Interior (Same-Side)
|
||
</td>
|
||
<td className="p-3">
|
||
Between the lines, same side of transversal
|
||
</td>
|
||
<td className="p-3 font-bold text-rose-700">
|
||
Supplementary (sum = 180°)
|
||
</td>
|
||
</tr>
|
||
<tr className="bg-emerald-50">
|
||
<td className="p-3 font-bold text-slate-600">
|
||
Vertical Angles
|
||
</td>
|
||
<td className="p-3">
|
||
Opposite each other at an intersection
|
||
</td>
|
||
<td className="p-3 font-bold text-emerald-700">Equal</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
|
||
{/* Worked Example */}
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-100">
|
||
<p className="font-bold text-emerald-800 mb-3">
|
||
Worked Example: Find All 8 Angles
|
||
</p>
|
||
<p className="text-sm text-slate-700 mb-2">
|
||
If one angle formed by a transversal cutting two parallel lines
|
||
is 65°, find all other angles.
|
||
</p>
|
||
<div className="bg-emerald-50 rounded-lg p-4 text-sm font-mono text-slate-700 space-y-1">
|
||
<p>
|
||
Angle 1 = <strong>65°</strong> (given)
|
||
</p>
|
||
<p>
|
||
Vertical angle = <strong>65°</strong> (vertical angles are
|
||
equal)
|
||
</p>
|
||
<p>
|
||
Corresponding angle = <strong>65°</strong> (corresponding
|
||
angles are equal)
|
||
</p>
|
||
<p>
|
||
Its vertical angle = <strong>65°</strong>
|
||
</p>
|
||
<p>
|
||
All four supplementary angles = 180° − 65° ={" "}
|
||
<strong>115°</strong>
|
||
</p>
|
||
<p className="mt-2 text-emerald-800 font-bold">
|
||
Result: four 65° angles and four 115° angles.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
<div className="bg-sky-50 border border-sky-200 rounded-xl p-4 text-sm">
|
||
<p className="font-bold text-sky-900 mb-1">
|
||
SAT Strategy: Label with x and 180 − x
|
||
</p>
|
||
<p className="text-slate-700">
|
||
When angles are expressed algebraically, label all equal angles
|
||
as "x" and all supplementary angles as "180 − x." Then set equal
|
||
or add to 180 to solve.
|
||
</p>
|
||
<div className="font-mono text-xs bg-white rounded p-2 mt-2 text-slate-700">
|
||
<p>
|
||
Example: Corresponding angles → 3x + 15 = 2x + 45 → x = 30°
|
||
</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<div className="mb-8">
|
||
<InteractiveTransversal />
|
||
</div>
|
||
|
||
<button
|
||
onClick={() => scrollToSection(1)}
|
||
className="group flex items-center text-emerald-600 font-bold hover:text-emerald-800"
|
||
>
|
||
Next: Triangles{" "}
|
||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||
</button>
|
||
</section>
|
||
|
||
{/* Section 2: Triangles */}
|
||
<section
|
||
ref={(el) => {
|
||
sectionsRef.current[1] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center mb-24"
|
||
>
|
||
<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
|
||
Triangle Theorems
|
||
</h2>
|
||
<div className="prose prose-slate text-lg text-slate-600 mb-8">
|
||
<p>
|
||
Two essential theorems unlock almost every SAT triangle problem.
|
||
The interactive tool below lets you drag vertices to verify both
|
||
dynamically.
|
||
</p>
|
||
</div>
|
||
|
||
<div className="bg-emerald-50 border border-emerald-200 rounded-2xl p-6 mb-8 space-y-5">
|
||
<h3 className="text-lg font-bold text-emerald-900">
|
||
Core Triangle Rules
|
||
</h3>
|
||
|
||
<div className="grid md:grid-cols-2 gap-4">
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-200">
|
||
<p className="font-bold text-emerald-900 mb-1">
|
||
Triangle Sum Theorem
|
||
</p>
|
||
<div className="font-mono text-center bg-emerald-50 py-2 rounded text-emerald-700 font-bold mb-2">
|
||
∠A + ∠B + ∠C = 180°
|
||
</div>
|
||
<p className="text-sm text-slate-700">
|
||
The three interior angles of any triangle always sum to
|
||
exactly 180°. No exceptions.
|
||
</p>
|
||
</div>
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-200">
|
||
<p className="font-bold text-emerald-900 mb-1">
|
||
Exterior Angle Theorem
|
||
</p>
|
||
<div className="font-mono text-center bg-emerald-50 py-2 rounded text-emerald-700 font-bold mb-2">
|
||
∠ext = ∠A + ∠B
|
||
</div>
|
||
<p className="text-sm text-slate-700">
|
||
An exterior angle equals the sum of the two non-adjacent
|
||
(remote) interior angles.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
{/* Worked Examples */}
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-100">
|
||
<p className="font-bold text-emerald-800 mb-3">Worked Examples</p>
|
||
<div className="space-y-3">
|
||
<div className="bg-emerald-50 rounded-lg p-4 text-sm">
|
||
<p className="font-semibold text-emerald-800 mb-1">
|
||
Example 1: Find a missing angle
|
||
</p>
|
||
<div className="font-mono text-xs text-slate-700 space-y-1">
|
||
<p>Two angles are 47° and 83°. Find the third.</p>
|
||
<p>
|
||
∠C = 180° − 47° − 83° ={" "}
|
||
<strong className="text-emerald-700">50°</strong>
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div className="bg-emerald-50 rounded-lg p-4 text-sm">
|
||
<p className="font-semibold text-emerald-800 mb-1">
|
||
Example 2: Exterior angle
|
||
</p>
|
||
<div className="font-mono text-xs text-slate-700 space-y-1">
|
||
<p>
|
||
Two interior angles are 40° and 65°. Find the exterior
|
||
angle at the third vertex.
|
||
</p>
|
||
<p>
|
||
∠ext = 40° + 65° ={" "}
|
||
<strong className="text-emerald-700">105°</strong>
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div className="bg-emerald-50 rounded-lg p-4 text-sm">
|
||
<p className="font-semibold text-emerald-800 mb-1">
|
||
Example 3: Isosceles triangle
|
||
</p>
|
||
<div className="font-mono text-xs text-slate-700 space-y-1">
|
||
<p>
|
||
An isosceles triangle has vertex angle = 40°. Find the
|
||
base angles.
|
||
</p>
|
||
<p>
|
||
Each base angle = <Frac n="180° − 40°" d="2" /> ={" "}
|
||
<Frac n="140°" d="2" /> ={" "}
|
||
<strong className="text-emerald-700">70°</strong>
|
||
</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
{/* Triangle Inequality */}
|
||
<div className="bg-sky-50 border border-sky-200 rounded-xl p-4 text-sm">
|
||
<p className="font-bold text-sky-900 mb-1">
|
||
Triangle Inequality Theorem
|
||
</p>
|
||
<p className="text-slate-700 mb-2">
|
||
Any two sides of a triangle must sum to more than the third
|
||
side.
|
||
</p>
|
||
<div className="font-mono text-xs bg-white rounded p-2 text-slate-700">
|
||
<p>a + b > c, a + c > b, b + c > a</p>
|
||
<p className="mt-1">
|
||
Example: Can a triangle have sides 3, 5, 9?
|
||
</p>
|
||
<p>3 + 5 = 8 < 9 → NO, not a valid triangle.</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<InteractiveTriangle />
|
||
|
||
<button
|
||
onClick={() => scrollToSection(2)}
|
||
className="mt-8 group flex items-center text-emerald-600 font-bold hover:text-emerald-800"
|
||
>
|
||
Next: Special Triangles{" "}
|
||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||
</button>
|
||
</section>
|
||
|
||
{/* Section 3: Special Triangles */}
|
||
<section
|
||
ref={(el) => {
|
||
sectionsRef.current[2] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center mb-24"
|
||
>
|
||
<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
|
||
Special Right Triangles
|
||
</h2>
|
||
<div className="prose prose-slate text-lg text-slate-600 mb-8">
|
||
<p>
|
||
These two triangle types appear constantly on the SAT. Memorize
|
||
their side ratios so you can find any missing side without using
|
||
the Pythagorean theorem.
|
||
</p>
|
||
</div>
|
||
|
||
<div className="bg-emerald-50 border border-emerald-200 rounded-2xl p-6 mb-8 space-y-5">
|
||
<h3 className="text-lg font-bold text-emerald-900">
|
||
The Two Special Right Triangles
|
||
</h3>
|
||
|
||
<div className="grid md:grid-cols-2 gap-4">
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-200">
|
||
<p className="font-bold text-emerald-900 mb-2">
|
||
45° — 45° — 90°
|
||
</p>
|
||
<div className="font-mono text-center bg-emerald-50 py-3 rounded text-emerald-700 font-bold text-lg mb-2">
|
||
Sides: 1 : 1 : √2
|
||
</div>
|
||
<p className="text-sm text-slate-700 mb-2">
|
||
Two equal legs. Hypotenuse = leg × √2.
|
||
</p>
|
||
<div className="font-mono text-xs bg-slate-50 rounded p-2 text-slate-700">
|
||
<p>If leg = 5: hyp = 5√2</p>
|
||
<p>
|
||
If hyp = 8: leg = <Frac n="8" d="√2" /> = 4√2
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-200">
|
||
<p className="font-bold text-emerald-900 mb-2">
|
||
30° — 60° — 90°
|
||
</p>
|
||
<div className="font-mono text-center bg-emerald-50 py-3 rounded text-emerald-700 font-bold text-lg mb-2">
|
||
Sides: 1 : √3 : 2
|
||
</div>
|
||
<p className="text-sm text-slate-700 mb-2">
|
||
Shortest leg opposite 30°. Hypotenuse = 2 × short leg.
|
||
</p>
|
||
<div className="font-mono text-xs bg-slate-50 rounded p-2 text-slate-700">
|
||
<p>Short leg = 4: long leg = 4√3, hyp = 8</p>
|
||
<p>Hyp = 10: short leg = 5, long leg = 5√3</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
{/* Pythagorean Theorem */}
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-100">
|
||
<p className="font-bold text-emerald-800 mb-3">
|
||
Pythagorean Theorem & Common Triples
|
||
</p>
|
||
<div className="font-mono text-center bg-emerald-50 py-2 rounded text-emerald-700 font-bold text-lg mb-3">
|
||
a² + b² = c²
|
||
</div>
|
||
<p className="text-sm text-slate-600 mb-3">
|
||
c is always the hypotenuse (opposite the right angle). Memorize
|
||
these Pythagorean triples — they appear frequently on the SAT:
|
||
</p>
|
||
<div className="overflow-x-auto rounded-xl border border-emerald-200">
|
||
<table className="w-full text-sm border-collapse">
|
||
<thead>
|
||
<tr className="bg-emerald-900 text-white">
|
||
<th className="p-2 text-center">Triple (a, b, c)</th>
|
||
<th className="p-2 text-center">Scaled Version</th>
|
||
<th className="p-2 text-center">Verify</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody className="divide-y divide-emerald-100">
|
||
<tr className="bg-white text-center">
|
||
<td className="p-2 font-bold">3, 4, 5</td>
|
||
<td className="p-2 text-slate-600">6-8-10, 9-12-15</td>
|
||
<td className="p-2 font-mono text-xs">9 + 16 = 25 ✓</td>
|
||
</tr>
|
||
<tr className="bg-emerald-50 text-center">
|
||
<td className="p-2 font-bold">5, 12, 13</td>
|
||
<td className="p-2 text-slate-600">10-24-26</td>
|
||
<td className="p-2 font-mono text-xs">
|
||
25 + 144 = 169 ✓
|
||
</td>
|
||
</tr>
|
||
<tr className="bg-white text-center">
|
||
<td className="p-2 font-bold">8, 15, 17</td>
|
||
<td className="p-2 text-slate-600">—</td>
|
||
<td className="p-2 font-mono text-xs">
|
||
64 + 225 = 289 ✓
|
||
</td>
|
||
</tr>
|
||
<tr className="bg-emerald-50 text-center">
|
||
<td className="p-2 font-bold">7, 24, 25</td>
|
||
<td className="p-2 text-slate-600">—</td>
|
||
<td className="p-2 font-mono text-xs">
|
||
49 + 576 = 625 ✓
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
</div>
|
||
|
||
{/* Worked examples */}
|
||
<div className="space-y-3">
|
||
<div className="bg-sky-50 rounded-xl p-4 border border-sky-200 text-sm">
|
||
<p className="font-semibold text-sky-800 mb-2">
|
||
Worked Example: 30-60-90
|
||
</p>
|
||
<div className="font-mono text-xs text-slate-700 space-y-1">
|
||
<p>
|
||
An equilateral triangle has side length 10. Find the height.
|
||
</p>
|
||
<p>The height bisects it into two 30-60-90 triangles.</p>
|
||
<p>Short leg (half the base) = 5</p>
|
||
<p>
|
||
Long leg (height) = 5√3 ≈{" "}
|
||
<strong className="text-sky-800">8.66</strong>
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div className="bg-sky-50 rounded-xl p-4 border border-sky-200 text-sm">
|
||
<p className="font-semibold text-sky-800 mb-2">
|
||
Worked Example: Pythagorean Triple
|
||
</p>
|
||
<div className="font-mono text-xs text-slate-700 space-y-1">
|
||
<p>
|
||
A right triangle has legs 9 and 12. Find the hypotenuse.
|
||
</p>
|
||
<p>Recognize: 9 and 12 are multiples of 3 and 4 (× 3).</p>
|
||
<p>
|
||
This is a 3-4-5 triple × 3: hypotenuse ={" "}
|
||
<strong className="text-sky-800">15</strong>
|
||
</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<button
|
||
onClick={() => scrollToSection(3)}
|
||
className="group flex items-center text-emerald-600 font-bold hover:text-emerald-800"
|
||
>
|
||
Next: Polygons{" "}
|
||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||
</button>
|
||
</section>
|
||
|
||
{/* Section 4: Polygons */}
|
||
<section
|
||
ref={(el) => {
|
||
sectionsRef.current[3] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center mb-24"
|
||
>
|
||
<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
|
||
Polygons
|
||
</h2>
|
||
<div className="prose prose-slate text-lg text-slate-600 mb-8">
|
||
<p>
|
||
Polygon angle rules extend triangle logic — any polygon can be
|
||
divided into triangles, which is where the interior angle sum
|
||
formula comes from.
|
||
</p>
|
||
</div>
|
||
|
||
<div className="bg-emerald-50 border border-emerald-200 rounded-2xl p-6 mb-8 space-y-5">
|
||
<h3 className="text-lg font-bold text-emerald-900">
|
||
Polygon Angle Formulas
|
||
</h3>
|
||
|
||
<div className="grid md:grid-cols-2 gap-4">
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-200">
|
||
<p className="font-bold text-emerald-900 mb-1">
|
||
Interior Angle Sum
|
||
</p>
|
||
<div className="font-mono text-center bg-emerald-50 py-2 rounded text-emerald-700 font-bold mb-2">
|
||
(n − 2) × 180°
|
||
</div>
|
||
<p className="text-xs text-slate-600">
|
||
n = number of sides. Triangle: 180° | Quadrilateral: 360° |
|
||
Pentagon: 540° | Hexagon: 720°
|
||
</p>
|
||
</div>
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-200">
|
||
<p className="font-bold text-emerald-900 mb-1">
|
||
Exterior Angle Sum
|
||
</p>
|
||
<div className="font-mono text-center bg-emerald-50 py-2 rounded text-emerald-700 font-bold mb-2">
|
||
Always = 360°
|
||
</div>
|
||
<p className="text-xs text-slate-600">
|
||
True for ALL convex polygons, regardless of n. Imagine walking
|
||
around the polygon — you turn a full circle.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
{/* Reference table */}
|
||
<div className="bg-white rounded-xl p-5 border border-emerald-100">
|
||
<p className="font-bold text-emerald-800 mb-3">
|
||
Quick Reference: Regular Polygons
|
||
</p>
|
||
<div className="overflow-x-auto rounded-xl border border-emerald-200">
|
||
<table className="w-full text-sm border-collapse">
|
||
<thead>
|
||
<tr className="bg-emerald-900 text-white">
|
||
<th className="p-2 text-center">Polygon</th>
|
||
<th className="p-2 text-center">Sides (n)</th>
|
||
<th className="p-2 text-center">Interior Sum</th>
|
||
<th className="p-2 text-center">Each Interior Angle</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody className="divide-y divide-emerald-100 text-center">
|
||
<tr className="bg-white">
|
||
<td className="p-2">Triangle</td>
|
||
<td className="p-2">3</td>
|
||
<td className="p-2">180°</td>
|
||
<td className="p-2">60°</td>
|
||
</tr>
|
||
<tr className="bg-emerald-50">
|
||
<td className="p-2">Quadrilateral</td>
|
||
<td className="p-2">4</td>
|
||
<td className="p-2">360°</td>
|
||
<td className="p-2">90°</td>
|
||
</tr>
|
||
<tr className="bg-white">
|
||
<td className="p-2">Pentagon</td>
|
||
<td className="p-2">5</td>
|
||
<td className="p-2">540°</td>
|
||
<td className="p-2">108°</td>
|
||
</tr>
|
||
<tr className="bg-emerald-50">
|
||
<td className="p-2">Hexagon</td>
|
||
<td className="p-2">6</td>
|
||
<td className="p-2">720°</td>
|
||
<td className="p-2">120°</td>
|
||
</tr>
|
||
<tr className="bg-white">
|
||
<td className="p-2">Octagon</td>
|
||
<td className="p-2">8</td>
|
||
<td className="p-2">1080°</td>
|
||
<td className="p-2">135°</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
</div>
|
||
|
||
{/* Formula for one angle */}
|
||
<div className="bg-slate-50 border border-slate-200 rounded-xl p-4 text-sm">
|
||
<p className="font-bold text-slate-800 mb-1">
|
||
Each Interior Angle of a Regular n-gon
|
||
</p>
|
||
<div className="font-mono text-center bg-white py-2 rounded text-slate-700 font-bold mb-2">
|
||
<Frac n="(n − 2) × 180°" d="n" />
|
||
</div>
|
||
<p className="text-slate-600 text-xs">
|
||
Example: Regular hexagon → <Frac n="(6 − 2) × 180°" d="6" /> ={" "}
|
||
<Frac n="720°" d="6" /> = <strong>120°</strong>
|
||
</p>
|
||
<p className="text-slate-600 text-xs mt-1">
|
||
Example: Regular octagon → <Frac n="(8 − 2) × 180°" d="8" /> ={" "}
|
||
<Frac n="1080°" d="8" /> = <strong>135°</strong>
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
<PolygonWidget />
|
||
|
||
<button
|
||
onClick={() => scrollToSection(4)}
|
||
className="mt-12 group flex items-center text-emerald-600 font-bold hover:text-emerald-800"
|
||
>
|
||
Next: Practice{" "}
|
||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||
</button>
|
||
</section>
|
||
|
||
{/* Section 5: Quiz */}
|
||
<section
|
||
ref={(el) => {
|
||
sectionsRef.current[4] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center"
|
||
>
|
||
<div className="flex items-center gap-4 mb-8">
|
||
<div className="p-3 bg-emerald-100 rounded-full">
|
||
<BookOpen className="w-8 h-8 text-emerald-600" />
|
||
</div>
|
||
<h2 className="text-4xl font-extrabold text-slate-900">
|
||
Practice Time
|
||
</h2>
|
||
</div>
|
||
|
||
{ANGLES_QUIZ_DATA.map((quiz, idx) => (
|
||
<div key={quiz.id} className="mb-12">
|
||
<div className="flex items-center gap-2 mb-4">
|
||
<span className="bg-slate-200 text-slate-600 text-xs font-bold px-2 py-1 rounded uppercase">
|
||
Question {idx + 1}
|
||
</span>
|
||
</div>
|
||
<Quiz data={quiz} />
|
||
</div>
|
||
))}
|
||
|
||
<div className="p-8 bg-emerald-900 rounded-2xl text-white text-center mt-12">
|
||
<h3 className="text-2xl font-bold mb-4">Topic Mastered!</h3>
|
||
<button
|
||
onClick={onFinish}
|
||
className="px-6 py-3 bg-white text-emerald-900 font-bold rounded-full hover:bg-emerald-50 transition-colors"
|
||
>
|
||
Finish Lesson ✓
|
||
</button>
|
||
</div>
|
||
</section>
|
||
</div>
|
||
</div>
|
||
);
|
||
};
|
||
|
||
export default LinesAnglesLesson;
|