[/quote]
,
,
and 
are parallel and the angles 
and 
are acute. Show that it is possible to divide the triangle 
into 4 disjoint triangle 
and the triangle 
into 4 disjoint triangles 
such that the triangles 
and 
are congruent for all 
.
Write only the answers to the questions given.
to be more exact:
in years 2002-08 time was 90' for part A and 120' for part B
red balls and 
white balls. Audi took two balls at once from inside the bag. The chance of taking two balls of the same color is ...
unit. The area of the hexagon is ...
and 
.
is ...
so that 
and 
is ...
,
,
,
has an average of 
and a median of 
.
are integers greater than 
which are four consecutive quarters of an arithmetic row with 
.
and 
are squares of two consecutive natural numbers, then the smallest value of 
is ...
,
and 
.
and 
lies on the line segment 
.
and 
.
is ...
meet 
for each natural number 
.
is ....
provided that the difference of any two numbers at least 
is ...
which satisfies 
are as many as ...
and 
.
.
is a point on the side extension 
is perpendicular to 
and 
.
is ...
consists of 
with 
positive reals is ....
with 
is ....
square units. Two plots are said to be neighbors if they both have one side in common. Initially, there are a total of 
coins on the chessboard where each coin is only loaded exactly on one square and each square can contain coins or blanks. At each turn. You must select exactly one plot that holds the minimum number of coins in the number of neighbors of the plot and then you must give exactly one coin to each neighbor of the selected plot. The game ends if you are no longer able to select squares with the intended conditions. The smallest number of 
such that
has side lengths 
,
.
inside 
,
,
and denote them as 
,
,
.
?
be non-negative real numbers such that 
Prove that
students, 
students play cricket, 
students play hockey and 
students play basketball. 
students play both basketball and hockey, 
students play both cricket and basketball, 
students play both cricket and hockey, and 
students play all three: basketball, hockey, and cricket. Find the number of students who do not play any game.
with odd integer side lengths is divided into small rectangles with integer side lengths. Prove that there is at least one among the small rectangles whose distances from the four sides of 
(the number of positive divisors of 
with its center 
.
and one moving point 
on 
.
is a fixed point on 
intersect
,
intersects 
at 
.
when 
such that:![\[
a^2 + b^2 \mid a^3 + b^3
\]](http://latex.artofproblemsolving.com/a/1/d/a1ddbd20c854e291da5670de449229d1664fa56c.png)
Y by
Hi everyone,
I'm struggling a lot with geometry. I've found algebra, number theory, and even calculus to be relatively intuitive. However, when I took geometry, I found it very challenging. I stumbled my way through the class and can do the basic 'textbook' geometry problems, but still struggle a lot with geometry in competitive math. I find myself consistently skipping the geometry problems during contests (even the easier/first ones).
It's difficult for me to see the solution path. I can do the simpler textbook tasks (eg. find congruent triangles) but not more complex ones (eg. draw these two lines to form similar triangles).
Do you have any advice, resources, or techniques I should try?
I'm struggling a lot with geometry. I've found algebra, number theory, and even calculus to be relatively intuitive. However, when I took geometry, I found it very challenging. I stumbled my way through the class and can do the basic 'textbook' geometry problems, but still struggle a lot with geometry in competitive math. I find myself consistently skipping the geometry problems during contests (even the easier/first ones).
It's difficult for me to see the solution path. I can do the simpler textbook tasks (eg. find congruent triangles) but not more complex ones (eg. draw these two lines to form similar triangles).
Do you have any advice, resources, or techniques I should try?
