Notes – Lesson 6.2
Geometry
Name _________________________________
Complete the proof.
1. ABCD is a parallelogram
1. Given
2. AB || _________
2. ________________________
3. BC || _________
3. ________________________
4.
 3 = __________
4. ________________________
5.
 1 = __________
5. ________________________
6. AC = AC
6. ________________________
7.  ABC =  CDA
7. ________________________
8. AB = _________
8. _______________________
9. BC = ________
9. ______________________
Theorem: __________________________________ sides of a parallelogram are ______________________________.
If ABCD is a parallelogram, then
Consecutive Angles:
Def: angles that share a sides and are ______________________________ (add up to 180 0)
From the picture above:
Examples:
1.

1 = _________
 A +  B = _____________
2.
 B + __________ = 180o
3.
 1 = _______,  2 = _______,  3 = ________
 1 = _______,  2 = _______,  3 = ________
Theorem. __________________________ angles of a parallelogram are _______________________.
Examples.
1.
2.
3.
 1 = _______,  2 = _______,  3 = ________  1 = _______,  2 = _______,  3 = _______  1 = _______,  2 = _______,  3 = _______
Proving a Rectangle and a Square.
Rectangle – a parallelogram with 4 right angles.
To Prove:
Opposite sides are _______________
Square – a parallelogram with 4 congruent sides and 4 right angles.
To Prove:
Opposite sides are ______________
Four 90o angles
All sides are ______________
Four 90o angles
Example. Prove this figure is a rectangle.
R(-2, -3), S(4, 0), T(3, 2), V(-3, -1)
Proof:
Parallel:
RS ________ = TV __________,
ST_________ = RV _______
Four 90oangles:
Slope of RS = ___________ Slope of ST = ______________
Therefore,
 R = ___________
Using our theorems from before,
 S = ___________,  T = ___________,  V = ______________
Using Algebra with the Theorems.
1.
2.
3.
Theorem. The _____________________________ of a parallelogram _______________ each other.
ABCD is a parallelogram. Therefore:
BO = ___________
AO = ___________
Examples.
1.
2.
3.
4. AC = 24
5. x = EG
6. IK = 35
7.
8.