Could someone help me out on this one..?

Prove that the diagonals of the square bisect the interior angles.

Question

Could someone help me out on this one..?

Prove that the diagonals of the square bisect the interior angles.

anonymous · Answer

attachment

anonymous · Answer

u can do it

anonymous · Answer

@lovemenplayhard aww thanks for the encouragement :DD

johnweldon1993 · Answer

alright lets see here :) first prove that triangles QTR and STR are congruent

anonymous · Answer

:D :D XD

anonymous · Answer

because of the 90 degree angle and the slash marks on the sides of both angles..?

johnweldon1993 · Answer

right ... both pairs of opposite angles are congruent and all of the sides are congruent
 right? so you proved that....

now ...what are the angles of triangle SPT and PQT?
what is the relationship between them?

anonymous · Answer

would it be a 45 45 90...? im just takin a guess here...

johnweldon1993 · Answer

lol, not literally solve for the angle....but the angles would be equal wouldn't they?

johnweldon1993 · Answer

that angle at P and that angle at Q...are equal correct?

anonymous · Answer

yes!

johnweldon1993 · Answer

alright :) so then you proved there are congruent triangles...angles....and those triangles and corresponding triangles form interior angles....they are bisected...and you have proved what you wanted to prove :)

in other words

the angles are equal ...because they are corresponding angles of two congruent triangles. Since they form interior angle, and they are bisected ...you have proved it :)