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Lesson 8-2 Parallelograms

Lesson 8-2 Parallelograms. Theorem 8.3 Opposite sides of a parallelogram are congruent Theorem 8.4 Opposite angles in a parallelogram are congruent Theorem 8.5 Consecutive angles in a parallelogram are supplementary. Theorems ( con’t ). Theorem 8.6

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Lesson 8-2 Parallelograms

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  1. Lesson 8-2 Parallelograms • Theorem 8.3 Opposite sides of a parallelogram are congruent • Theorem 8.4 Opposite angles in a parallelogram are congruent • Theorem 8.5 Consecutive angles in a parallelogram are supplementary

  2. Theorems (con’t) • Theorem 8.6 If a parallelogram has one right angle, it has four right angles • Theorem 8.7 The diagonals of a parallelogram bisect each other • Theorem 8.8 Each diagonal of a parallelogram separates the parallelogram into two congruent triangles.

  3. Given: Prove: Example 2-1a Prove that if a parallelogram has two consecutive sides congruent, it has four sides congruent.

  4. Proof: Statements Reasons 1. 1. Given 2. 2. Given 3. 3. Opposite sides of a parallelogram are . 4. 4. Transitive Property Example 2-1b

  5. Prove that if and are the diagonals of , and Given: Prove: Example 2-1c

  6. Proof: Statements Reasons 1. 1. Given 2. 2. Opposite sides of a parallelogram are congruent. 3. 3. If 2 lines are cut by a transversal, alternate interior s are . 4. 4. Angle-Side-Angle Example 2-1d

  7. RSTU is a parallelogram. Find and y. If lines are cut by a transversal, alt. int. Example 2-2a Definition of congruent angles Substitution

  8. Example 2-2b Angle Addition Theorem Substitution Subtract 58 from each side.

  9. Answer: Example 2-2c Definition of congruent segments Substitution Divide each side by 3.

  10. ABCD is a parallelogram. Answer: Example 2-2d

  11. MULTIPLE-CHOICE TEST ITEMWhat 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)? A B C D Read the Test ItemSince the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of Example 2-3a

  12. Find the midpoint of Midpoint Formula Example 2-3b Solve the Test Item The coordinates of the intersection of the diagonals of parallelogram MNPR are (1, 2). Answer: C

  13. MULTIPLE-CHOICE TEST ITEMWhat 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)? A B C D Example 2-3c Answer: B

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