Prove A ≅ F Given parallelograms ABCD and CEFG… E F B C G A D Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms Given parallelograms ABCD and CEFG… A B C D E F G Prove A ≅ F

Objective Determine if a quadrilateral is a parallelogram. Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms Objective Determine if a quadrilateral is a parallelogram.

You have learned to identify the properties of a parallelogram. Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms You have learned to identify the properties of a parallelogram. Now you will be given the properties of a quadrilateral and will have to decide if the quadrilateral is a parallelogram. To do this, you can use the definition of a parallelogram or the conditions that follow. REMINDER…the definition of a parallelogram is a quadrilateral with two pairs of opposite sides parallel. REMEMBER…only one of the following conditions need to be met.

Conditions for a parallelogram. Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms Conditions for a parallelogram. 1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite angles are congruent. 3. One pair of opposite sides are both congruent and parallel. 4. If the diagonals bisect each other. 5. If an angle is supplementary to both of its consecutive angles.

Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms What values of x and y are necessary to make the figure a parallelogram? (2y2-2)° (139-2x)° (3x+6y+25) ° (-5y+1)°

Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms What values of a and b are necessary to make the figure a parallelogram? 2b-6 2a+10 4a 3a + 7

Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms What values of a and b are necessary to make the figure a parallelogram? 2a+b-8 (5a+2b+7)° 3a-30 (8a-3b)°

A quadrilateral has vertices A(2, 3), B(6, 2), C(5, 0), D(1, 1). Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms A quadrilateral has vertices A(2, 3), B(6, 2), C(5, 0), D(1, 1). How could you show that quadrilateral ABCD is a parallelogram?

Objectives Vocabulary Unit 6 – Polygons and Quadrilaterals 6.4 Properties of Special Parallelograms Objectives Apply properties of rectangles, rhombuses, and squares. Vocabulary rectangle rhombus square

A rectangle is a quadrilateral with four right angles. Unit 6 – Polygons and Quadrilaterals 6.4 Properties of Special Parallelograms A rectangle is a quadrilateral with four right angles. Theorem: The diagonals of a rectangle are congruent AC  BD If a quadrilateral is a rectangle, then it is a parallelogram

Prove the diagonals of a rectangle are congruent. Unit 6 – Polygons and Quadrilaterals 6.4 Properties of Special Parallelograms Prove the diagonals of a rectangle are congruent.

The diagonals of a rhombus are perpendicular Unit 6 – Polygons and Quadrilaterals 6.4 Properties of Special Parallelograms A rhombus is a quadrilateral with four congruent sides. Theorems: The diagonals of a rhombus are perpendicular The diagonals of a rhombus bisect the angles If a quadrilateral is a rhombus, then it is a parallelogram

TVWX is a rhombus. Find everything you can! Unit 6 – Polygons and Quadrilaterals 6.4 Properties of Special Parallelograms TVWX is a rhombus. Find everything you can! 2 3 4

Unit 6 – Polygons and Quadrilaterals 6 Unit 6 – Polygons and Quadrilaterals 6.4 Properties of Special Parallelograms A square is a quadrilateral with four right angles and four congruent sides. A square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

POLYGONS QUADRILATERALS PARALELLOGRAMS RHOMBUS Opp sides congruent 4 sided figure QUADRILATERALS No pair of parallel sides. 2 pairs of adjacent congruent sides 1 pair of opp. sides parallel 2 pairs of opp. sides parallel Opp sides congruent Opp angles congruent Diag. bisect each other TRAPEZOID PARALELLOGRAMS KITE 4 congruent sides 4 right angles Legs congruent Diag perpendicular One opp pair angles ≈ Other opp pair angles bisected by diag ISOS. TRAPEZOID RHOMBUS RECTANGLE Base angles congruent Diagonals congruent Legs congruent Diag bisect angle Diag perpendicular Diag bisect angle Diag perpendicular Diag congruent Diag congruent SQUARE

HOMEWORK: 6.3(414): 11-14,17-19,21-23,35,36 6.4(424): 10-15,19-31(odds),40-42