Lesson 2 Menu 1.Find the measure of an interior angle of a regular polygon with 10 sides. 2.Find the measure of an interior angle of a regular polygon.

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6-2 Properties of Parallelograms

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Presentation transcript:

Lesson 2 Menu 1.Find the measure of an interior angle of a regular polygon with 10 sides. 2.Find the measure of an interior angle of a regular polygon with 12 sides. 3.Find the sum of the measures of the interior angles of a convex 20-gon. 4.Find the sum of the measures of the interior angles of a convex 16-gon.

Lesson 2 MI/Vocab Recognize and apply properties of the sides and angles of parallelograms. Recognize and apply properties of the diagonals of parallelograms.

Lesson 2 TH1

Lesson 2 Ex1 Proof of Theorem 6.4 Prove that if a parallelogram has two consecutive sides congruent, it has four sides congruent. Given: Prove:

Lesson 2 Ex1 Proof of Theorem Given Proof: ReasonsStatements 4.Transitive Property4. 2.Given2. 3.Opposite sides of a parallelogram are . 3.

Lesson 2 CYP1

A.A B.B C.C D.D Lesson 2 CYP1 A. SSSB. ASA C. SASD. AAS Proof: ReasonsStatements 1. Given Opposite sides of a parallelogram are congruent ________________ 4. ΔBEC  ΔDEA, ΔBEA  ΔDEC ? 3.If 2 lines are cut by a transversal, alternate interior s are . 3.

Lesson 2 Ex2 Quadrilateral RSTU is a parallelogram. Find m  URT, m  RST, and y. Properties of Parallelograms If lines are cut by a transversal, alternate interior Definition of congruent angles Substitution

Lesson 2 Ex2 Properties of Parallelograms Angle Addition Postulate Substitution Subtract 58 from each side.

Lesson 2 Ex2 Answer: m  URT = 40, m  RST = 122, y = 6 Properties of Parallelograms Substitution Divide each side by 3. Definition of congruent segments

Lesson 2 CYP2 1.A 2.B 3.C 4.D A.54 B.64 C.62 D.58 ABCD is a parallelogram. Find m  BDC.

Lesson 2 CYP2 1.A 2.B 3.C 4.D A.54 B.64 C.62 D.58 ABCD is a parallelogram. Find m  BCD.

Lesson 2 CYP2 1.A 2.B 3.C 4.D A.4 B.5 C.8 D.20 ABCD is a parallelogram. Find x.

Lesson 2 TH2

Lesson 2 Ex3 Diagonals of a Parallelogram A B C D 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)? Read the Item Since the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of

Lesson 2 Ex3 Solve the Item Answer: C Diagonals of a Parallelogram Find the midpoint of The coordinates of the intersection of the diagonals of parallelogram MNPR are (1, 2). Midpoint Formula

1.A 2.B 3.C 4.D Lesson 2 CYP3 What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with vertices L(0, –3), M(–2, 1), N(1, 5), O(3, 1)? A. B. C. D.

Lesson 2 TH3