LESSON 39: DIFFERENCE OF TWO SQUARES, PARALLELOGRAM PROOF, RHOMBUS

If both terms of a two term algebraic sum are identical except that the sign of the second term is different, we say that each expression is the conjugate of the other expression.

-2x – 3y is the conjugate of -2x + 3y -2x + 3y is the conjugate of -2x – 3y 3x + 4 is the conjugate of 3x - 4 3x – 4 is the conjugate of 3x + 4

When conjunctions are multiplied, the product does not have a middle term, as seen here. (-2x – 3y)(-2x + 3y) = 4x – 9y (3x – 4)(3x + 4) = 9x –

Example: Solve by factoring: 4x – 9 = 0 2

Answer: x = 3/2, -3/2

Example: Solve by factoring 81m – 25 = 0 2

Answer: m = -5/9, 5/9

We remember that a parallelogram is defined to be a quadrilateral with two pairs of parallel sides. Also recall that a parallelogram has four properties, which are listed as follows.

1.The sides opposite each other have equal lengths 2.The angles opposite each other have equal measures 3.The sum of any two consecutive angles is 180 degrees 4.The diagonals bisect each other

A rhombus is a parallelogram that has three additional properties. The first is the definition of a rhombus the other two properties are theorems and can be proved.

1.A rhombus is a parallelogram whose four sides have equal lengths 2.The diagonals of a rhombus bisect the angles of the rhombus 3.The diagonals of a rhombus are perpendicular bisectors of each other

Example: DEFG is a rhombus. The measure of the reflex angle is 280 degrees. Find A, X, B, K, and C. E F D G 280° X° A° C° B° K°

Answer: X = 40 A= 40 K = 50 B = 50 C = 90

HW: Lesson 39 #1-30