Proof

1- prove that a non-simple puadrilateral can be inscribed in a circle <=> opposite angles are equal (both direction)

Polygons

Show that the number of diagonals in a polygon is never the same as the sum of the measures of the exterior angles, one per vertex, of the polygon.

Proof

If O is an interior point of triangle ABC prove that OA+OB+OC a- is greater than 1/2 (perimeter of triangle ABC) b- is less than the perimeter of triangle ABC

Proof

BE is a median of triangle ABC. The line through C and the midpoint H of BE meets AB at F. prove that AF/FB=2. You must use a parallogram proof hint: extend BE to 3/2 of its lenght

Proof

Given triangle ABC where BC=CD prove that if x>y then y is less than z (see attachment)

Proof

Prove the first half of the open-jaw inequality where the point G lies inside triangle DEF i.e show that if x less than y => AC < DF (see attachment)

Proof

Use the side-angle inequality to show that in triangle ABC if the internal bisectore of angle A meets BC at D and AB>AC , then DB>DC

Proof

ABCD is a convex quadrilateral and F and H are the midpoint of BC and AD respectively. If AC cuts FH at the midpoint K of FH show that [ABC]=[ADC] ( [] = area)

Proof

ABCD is a convex quadralteral as shown in document and E,F,G,H are midpoints of AB,BC,CD,DA. EG cuts FH at K prove that [AEKH]+[CGKF]=[BFKE]+[DHKG]

Proof

Given the figure in document with 3BF=2FC , AE=2EF and [DEF]=1 a- FIND [DFC] b-FIND AC/AD