Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "User:Afly"

(Created page with "==Afly== <asy> pair A=(0,0); pair B=(2,0); pair C=(1,sqrt(3)); draw(A--B--C); draw(A--C--B); </asy> <math> \text{That is a equilateral triangle with side length 2!} </math>...")
 
(→‎Afly)
Line 1: Line 1:
−
==Afly==
+
==About Afly==
 +
 
 +
==Some of my asymptote creations==
  
 
<asy>
 
<asy>
Line 51: Line 53:
 
<math>
 
<math>
 
\text{The area is } 1 \cdot 2 \cdot \frac{1}{2} = \boxed{1}
 
\text{The area is } 1 \cdot 2 \cdot \frac{1}{2} = \boxed{1}
 +
</math>
 +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 +
<asy>
 +
pair A=(0,0);
 +
pair B=(0,3);
 +
pair C=(4,0);
 +
draw(A--B--C--A,black+linewidth(1));
 +
pair D=(-3,0);
 +
pair E=(-3,3);
 +
draw(A--B--E--D--A,red+linewidth(1));
 +
pair F=(0,-4);
 +
pair G=(4,-4);
 +
draw(A--C--G--F--A,orange+linewidth(1));
 +
pair H=(7,4);
 +
pair I=(3,7);
 +
draw(B--C--H--I--B,yellow+linewidth(1));
 +
draw(A--B--C--A,black+linewidth(1));
 +
</asy>
 +
<math>
 +
\text{The pythagorean theorem: red plus orange equals yellow}
 +
</math>
 +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 +
<asy>
 +
pair A=(0,0);
 +
pair B=(10,0);
 +
pair C=(6,8);
 +
pair D=(2,8);
 +
pair E=(30/7,40/7);
 +
draw(A--B--C--D--A,black+linewidth(5));
 +
fill(A--E--D--cycle,red);
 +
fill(B--E--C--cycle,yellow);
 +
dot(A);
 +
dot(B);
 +
dot(C);
 +
dot(D);
 +
dot(E);
 +
label(A,'A',SW);
 +
label(B,'B',SE);
 +
label(C,'C',NE);
 +
label(D,'D',NW);
 +
label(E,'E',S);
 +
draw(A--E--C,blue+linewidth(2));
 +
draw(B--E--D,blue+linewidth(2));
 +
</asy>
 +
<math>
 +
\text{Given that } AB \parallel DC \text{ , prove that } A _ \triangle AED = A  _ \triangle BEC .
 
</math>
 
</math>

Revision as of 18:31, 12 November 2023

About Afly

Some of my asymptote creations

[asy] pair A=(0,0); pair B=(2,0); pair C=(1,sqrt(3)); draw(A--B--C); draw(A--C--B); [/asy]

$\text{That is a equilateral triangle with side length 2!}$

$\text{The height is } \sqrt{2^2-1^2} = \sqrt{3}$

$\text{The area is } 2 \cdot \sqrt{3} \cdot \frac{1}{2} = \boxed{\sqrt{3}}$

$\dots$

[asy] pair A=(0,0); pair B=(0,2); pair C=(1,1); draw(A--B--C); draw(A--C--B); [/asy]

$\text{Homework: calculate the area}$

ANSWER: LOOK ONLY WHEN THE PROBLEM IS COMPLETED >>> THIS IS ONLY TO CHECK YOUR ANSWER

$\text{This is an isosceles right triangle. It has side length }\sqrt{2}$

$\text{It has an height of } \frac{\sqrt{2}}{\sqrt{2}} = 1 \text{ and a base of } \sqrt{2} \cdot \sqrt{2} = 2$

$\text{The area is } 1 \cdot 2 \cdot \frac{1}{2} = \boxed{1}$ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ [asy] pair A=(0,0); pair B=(0,3); pair C=(4,0); draw(A--B--C--A,black+linewidth(1)); pair D=(-3,0); pair E=(-3,3); draw(A--B--E--D--A,red+linewidth(1)); pair F=(0,-4); pair G=(4,-4); draw(A--C--G--F--A,orange+linewidth(1)); pair H=(7,4); pair I=(3,7); draw(B--C--H--I--B,yellow+linewidth(1)); draw(A--B--C--A,black+linewidth(1)); [/asy] $\text{The pythagorean theorem: red plus orange equals yellow}$ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ [asy] pair A=(0,0); pair B=(10,0); pair C=(6,8); pair D=(2,8); pair E=(30/7,40/7); draw(A--B--C--D--A,black+linewidth(5)); fill(A--E--D--cycle,red); fill(B--E--C--cycle,yellow); dot(A); dot(B); dot(C); dot(D); dot(E); label(A,'A',SW); label(B,'B',SE); label(C,'C',NE); label(D,'D',NW); label(E,'E',S); draw(A--E--C,blue+linewidth(2)); draw(B--E--D,blue+linewidth(2)); [/asy] $\text{Given that } AB \parallel DC \text{ , prove that } A _ \triangle AED = A _ \triangle BEC .$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=User:Afly&oldid=202773"