HELP FAST Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE CE and BE DE
Angles Segments Triangles Statements Reasons
ABCD is a parallelogram
ZABE and CDE
are alt. interior angles
ZBCE and ZDAE
2CBE and ZADE
are alt, interior angles are alt, interior angles
ZBAE and ZDCE
are alt, interior angles
B
С
Reasons
1. given
2. def. of alt, interior angles
Statements
1. ABCD is a parallelogram
2. ZABE and ZCDE
are alt. interior angles
3. ZBAE and ZDCE
are alt. interior angles
4. AB CD
5. AB || CD
6. ZBAEZDCE
3. def. of alt, interior angles
D
4. parallelogram side theorem
5. def. of parallelogram
6. alternate interior angles theorem
Think about the properties of alternate
interior angles