Waste less time on Facebook — follow Brilliant.
×

90 is not equal 90

Given that \(AB=DC,DA \)perpendicular to \(AB\) . Let M and N be the perpendicular bisector of \(AD\) and \(BC\) respectively. These two perpendicular bisector intersect in \(E\). Joining \(AE,ED,EB,EC\) since \(EM\) is perpendicular bisector \(AE=ED\) since \(EN\) is perpendicular bisector \(EB=EC\) \(\triangle EAB=\triangle EDC\) (SSS) \(\angle EAB=\angle EDC\) \(\angle EAD=\angle EDA\) we have \(\angle MAB=\angle MDC\) obviously it is impossible.

Note by Choi Chakfung
1 year, 6 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Here's an accurate graphic of how it should look like

We can see that \(\Delta ABE\) is congruent with \(\Delta DCE\), and the paradox then vanishes.

Michael Mendrin - 1 year, 6 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...