assume that "diagonals are not congruent in a rectangle". By definition of rectangle, it has four right angles and opposite sides are congruent. So, by pythagorean theorem, AB^2 + BC^2 = AC^2 and BC^2 + CD^2 = BD^2. Since opposite sides are congruent, AB=CD, AD = BC. By substitution BC^2 = BD^2. that means diagonals are congruent. Thats a contradiction to what we have assumed. so the initial assumption must be wrong, and the opposite of that must be correct. So, the diagonals of rectangle are congruent.

@ganeshie8

Question

assume that "diagonals are not congruent in a rectangle". By definition of rectangle, it has four right angles and opposite sides are congruent. So, by pythagorean theorem, AB^2 + BC^2 = AC^2 and BC^2 + CD^2 = BD^2. Since opposite sides are congruent, AB=CD, AD = BC. By substitution BC^2 = BD^2. that means diagonals are congruent. Thats a contradiction to what we have assumed. so the initial assumption must be wrong, and the opposite of that must be correct. So, the diagonals of rectangle are congruent.

@ganeshie8

anonymous · Answer

can you help with this please

ganeshie8 · Answer

yeah ?

anonymous · Answer

sorry i copied the wrong thing

ganeshie8 · Answer

:) i guessed that lol

anonymous · Answer

Matt is constructing two similar triangles for an art project. The drawing below shows Matt's plans, but there is an error in his drawing. What changes would he make to the dimensions to change the error? Explain your reasoning using complete sentences.

ganeshie8 · Answer

find the ratios of corresponding sides first

ganeshie8 · Answer

if the triangles are similar we should get same number for all ratios

anonymous · Answer

ok how wwould i go about finding the ratios

ganeshie8 · Answer

we should get below ratios same :

$\large \frac{13}{2.5} = \frac{20.8}{4} = \frac{43}{8.4}$

ganeshie8 · Answer

use ur calculator and simplify each ratio

anonymous · Answer

ok

ganeshie8 · Answer

$\large \frac{13}{2.5} = \frac{20.8}{4} = \frac{43}{8.4}$


$\large 5.2 = 5.2 = 5.119$

ganeshie8 · Answer

clearly, first two ratios are matching exactly.
there seems to be a problem wid third ratio, eh ?

anonymous · Answer

yea thats wat i got

ganeshie8 · Answer

since the correct ratio is $5.2$, we want third ratio also to equal this :

say, we want to change the side DF from 43 to fix this error, then :

$\large \frac{DF}{8.4} = 5.2$

$\large DF  = 43.68$

ganeshie8 · Answer

So, to fix the error, we need to change DF from 43 to 43.68

anonymous · Answer

ok and how can we do that?

ganeshie8 · Answer

we're done !

ganeshie8 · Answer

the question is just asking us to find out wat changes he needs to do to the dimensions.

ganeshie8 · Answer

we concluded he needs to change DF from 43 to 43.68. so we're done !

anonymous · Answer

ooh ok well thank you but i have more if you have the time

ganeshie8 · Answer

post them in another thread
il try if im awake... it 1am here in india lol :)

anonymous · Answer

ooh