lesson 8-2 parallelograms
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Lesson 8-2 Parallelograms
• Theorem 8.3Opposite sides of a parallelogram are congruent• Theorem 8.4Opposite angles in a parallelogram are
congruent• Theorem 8.5Consecutive angles in a parallelogram are
supplementary
Theorems (con’t)
• Theorem 8.6If a parallelogram has one right angle, it has four
right angles• Theorem 8.7The diagonals of a parallelogram bisect each other• Theorem 8.8Each diagonal of a parallelogram separates the
parallelogram into two congruent triangles.
Prove that if a parallelogram has two consecutive sides congruent, it has four sides congruent.
Given:
Prove:
1. 1. Given
Proof:
ReasonsStatements
4. Transitive Property4.
2. Given2.
3. Opposite sides of a parallelogram are .
3.
Given:
Prove:
Prove that if and are the diagonals of , and
Proof:
ReasonsStatements
1. Given1.
4. Angle-Side-Angle4.
2. Opposite sides of a parallelogram are congruent.
2.
3. If 2 lines are cut by a transversal, alternate interior s are .
3.
If lines are cut by a transversal, alt. int.
Definition of congruent angles
Substitution
RSTU is a parallelogram. Find and y.
Angle Addition Theorem
Substitution
Subtract 58 from each side.
Substitution
Divide each side by 3.
Definition of congruent segments
Answer:
ABCD is a parallelogram.
Answer:
Read the Test ItemSince the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of
A B C D
MULTIPLE-CHOICE TEST ITEM What are the coordinates of the intersection of the diagonals of parallelogram MNPR, with vertices M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)?
Solve the Test Item
Find the midpoint of
The coordinates of the intersection of the diagonals of parallelogram MNPR are (1, 2).
Answer: C
Midpoint Formula
Answer: B
A B C D
MULTIPLE-CHOICE TEST ITEM What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with verticesL(0, –3), M(–2, 1), N(1, 5), O(3, 1)?
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