Proving the Parallelogram Diagonal Theorem Try it
Angles Segments Triangles Statements Reasons
SIRE
Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE CE and BE DE
ASA
CPCTC
VX
B
с
given
alternate interior angles theorem
E
Reasons
1. given
2. def. of alt, interior angles
Statements
✓ 1. ABCD is a parallelogram
✓ 2. ZABE and ZCDE
are alt. interior angles
✓ 3. AB CD
✓ 4. AB || CD
✓ 5. ZABEZCDE
✓ 6. Z BAE and ZDCE
are alt. interior angles
3. parallelogram side theorem
4. def. of parallelogram
5. alternate interior angles theorem
6. def. of alt, interior angles
A
D
Think about the properties of alternate
interior angles