Help.
Prove that the diagonals of the square bisect the interior angles.
(picture attached)

Question

Help.
Prove that the diagonals of the square bisect the interior angles.
(picture attached)

anonymous · Answer

attachment

jim766 · Answer

Start with the square what do you know about squares?

anonymous · Answer

squares have 4 sides, 4 right angles and the sides are congruent.

anonymous · Answer

and the sides are parallel to each other

jim766 · Answer

so if all 4 sides are congruent...can you see how the triangles are the same?

anonymous · Answer

yes

jim766 · Answer

what kind of triangles are they

jim766 · Answer

what kind of angle do the all have in common?

jim766 · Answer

the angle in the center

anonymous · Answer

equilateral triangles

jim766 · Answer

they are not equalateral...because their sides are different lengths
but they do have a right angle

anonymous · Answer

they are right triangles

jim766 · Answer

yep...which means that center angle is 90  degress, right?

anonymous · Answer

yes

anonymous · Answer

does that prove my question?

jim766 · Answer

not yet....how many degrees in a trangle?

anonymous · Answer

180

jim766 · Answer

if the two corner angles are the same  what would they have t be?

jim766 · Answer

the corner angles of the triangle...just look at the bottom one for now

anonymous · Answer

they would be 45 degrees each

jim766 · Answer

right.......and if a square has 90 degree angles like you said...
the bottom angle cuts it in half...bisects it

jim766 · Answer

45 and 45

anonymous · Answer

oh ok! thanks! :)