Parallelogram Lesson purpose Educational to study definition

"Parallelogram"

Lesson purpose Educational: to study definition and a sign of a parallelogram, to learn to build a parallelogram; Developing: education of sense of beauty, interest in a subject, collectivism, mutual aid. Cultivate: development of logical thinking, creative thinking, ability to analyze, development of spatial representations, the mathematical speech.

Plan of the lesson: 1. Definition 2. Properties and sign 3. Tasks

Definition of parallelogram The parallelogram is a quadrangle at which the opposite sides are in pairs parallel (lie on parallel straight lines).

Properties of a parallelogram • The opposite sides are equal; • opposite corners, are also equal; ; • the sum of the corners adjacent to one party equals 180 degrees; • the sum of all corners will be 360 degrees; • diagonals are crossed, and divided by a point of intersection in half; • diagonals divide a parallelogram into 2 triangles which are equal among themselves; • the point of intersection of diagonals will be his center of symmetry; • the corner between heights will be equal to his acute angle; • bisectors of 2 opposite corners are parallel.

Parallelogram signs 1. When the quadrangle has the parties from which two equal and two parallel, this quadrangle will be a parallelogram; 2. In case the quadrangle has in pairs equal opposite sides, then it is a parallelogram; 3. Also, this figure will be a parallelogram when at a quadrangle of his diagonal are crossed, and the point of intersection divides them in half.

Parallelogram diagonals Diagonal of a parallelogram is called any piece connecting two tops of opposite corners of a parallelogram. The parallelogram has two diagonals - long d 1, and short - d 2

Parallelogram perimeter Perimeter of a parallelogram is called the sum of lengths of all parties of a parallelogram

Area of a parallelogram The area of a parallelogram is called the space limited by the parties of a parallelogram, i. e. within parallelogram perimeter.

Task 1

One of corners of a parallelogram is equal 65 °. To find other corners of a parallelogram. Decision. ∠C = ∠ A = 65 ° as opposite corners of a parallelogram. ∠А + ∠ In = 180 ° as corners, adjacent to one party of a parallelogram. ∠В = 180 ° — ∠А = 180 ° — 65 ° = 115 °. ∠D = ∠ B = 115 ° as opposite corners of a parallelogram. Answer: ∠А = ∠ With = 65 °; ∠В = ∠ D = 115 °.

Task 2 The sum of two corners of a parallelogram is equal 220 °. To find parallelogram corners. Decision. As the parallelogram has 2 equal acute angles and 2 equal obtuse angles, to us the sum of two obtuse angles, i. e. ∠В + ∠ is given D = 220 °. Then ∠В = ∠ D = 220 °: 2 = 110 °. ∠А + ∠ In = 180 ° as corners, adjacent to one party of a parallelogram, therefore ∠А = 180 ° — ∠В = 180 ° — 110 ° = 70 °. Then ∠C = ∠ A = 70 °. Answer: ∠А = ∠ With = 70 °; ∠В = ∠ D = 110 °.