Given: ABCD is a parallelogram. Diagonals AC, BD intersect at E.
Prove: AE CE and BE S DE
Angles Segments Triangles Statements Reasons
ASA
parallelogram side theorem
✓x
B
с
def. of alt, interior angles
alternate interior angles theorem
E
Statements
v 1. ABCD is a parallelogram
✓ 2. AB || CD
3. Z BAE and ZDCE
are alt, interior angles
Reasons
1. given
2. def. of parallelogram
3. def. of alt, interior angles
A
D
alternate interior angles theorem
Think about the properties of alternate
interior angles.

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