# Difference between revisions of "Wooga Looga Theorem"

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This lemma sucks. Adihaya Jayasharmaramankumarguptareddybavarajugopal's Lemme is way better, as it trivializes every problem -Heavytoothpaste | This lemma sucks. Adihaya Jayasharmaramankumarguptareddybavarajugopal's Lemme is way better, as it trivializes every problem -Heavytoothpaste | ||

@above, this is a Theorem which is different than a Lemma thonk -franzi | @above, this is a Theorem which is different than a Lemma thonk -franzi | ||

+ | |||

+ | This Theorem is literally false. Fix it. |

## Revision as of 20:46, 29 October 2020

## Contents

# Definition

If there is and points on the sides such that , then the ratio

Created by the Ooga Booga Tribe of the Caveman Society, https://www.youtube.com/channel/UC50E9TuLIMWbOPUX45xZPaQ

# Application 1

## Problem

The Wooga Looga Theorem states that the solution to this problem by franzliszt:

In points are on sides such that . Find the ratio of to .

## Solution 1

is this solution by RedFireTruck:

WLOG let , , . Then by Shoelace Theorem and , , . Then by Shoelace Theorem. Therefore the answer is .

## Solution 2

or this solution by franzliszt:

We apply Barycentric Coordinates w.r.t. . Let . Then we find that . In the barycentric coordinate system, the area formula is where is a random triangle and is the reference triangle. Using this, we find that

## Solution 3

or this solution by aaja3427:

According the the Wooga Looga Theorem, It is . This is

## Solution 4

or this solution by ilovepizza2020:

We use the to instantly get . (Note: You can only use this method when you are not in a contest as this method is so overpowered that the people behind tests decided to ban it.)

## Solution 5

or this solution by eduD_looC:

This is a perfect application of the Adhiytaha Anweopifanwpuiefhbavpwiuefnapveuihfnpvwheibfpanuwvfaw Lemma, which results in the answer being . A very beautiful application, which leaves graders and readers speechless.

# Application 2

## Problem

The Wooga Looga Theorem states that the solution to this problem by Matholic:

The figure below shows a triangle ABC whose area is 72cm2. If AD: DB = BE: EC =CF: FA =1: 5, find the area of triangle DEF

## Solution

is this solution by franzliszt:

We apply Barycentric Coordinates w.r.t. . Let . Then we find that . In the barycentric coordinate system, the area formula is where is a random triangle and is the reference triangle. Using this, we find that so .

# Application 3

## Problem

The Wooga Looga Theorem states that the solution to this problem by RedFireTruck:

Find the ratio if and in the diagram below.

## Solution 1

is this solution by franzliszt:

By the Wooga Looga Theorem, . Notice that is the medial triangle of **Wooga Looga Triangle ** of . So and by Chain Rule ideas.

## Solution 2

or this solution by franzliszt:

Apply Barycentrics w.r.t. so that . Then . And .

In the barycentric coordinate system, the area formula is where is a random triangle and is the reference triangle. Using this, we find that

# Testimonials

The Wooga Looga Theorem can be used to prove many problems and should be a part of any geometry textbook. ~ilp2020

The Wooga Looga Theorem is amazing and can be applied to so many problems and should be taught in every school. - RedFireTruck

The Wooga Looga Theorem is the best. -aaja3427

This lemma sucks. Adihaya Jayasharmaramankumarguptareddybavarajugopal's Lemme is way better, as it trivializes every problem -Heavytoothpaste

@above, this is a Theorem which is different than a Lemma thonk -franzi

This Theorem is literally false. Fix it.