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)?