6-2 Properties of Parallelograms

Slides:

Advertisements

Similar presentations

6.3 Proving that a Quadrilateral is a Parallelogram

Advertisements

6-2 Properties of Parallelograms page 294

Proving Quadrilaterals are Parallelograms Lesson 6.3 Chapter 6 Section 6.3 Proving Quadrilaterals Are Parallelograms.

Angles and Parallel Lines

Proving that a Quadrilateral is a Parallelogram

6.2 Properties of Parallelograms

6-3 Proving That a Quadrilateral Is a Parallelogram

Proving Quadrilaterals are Parallelograms - Sec 6.3 GOALS: To prove a quadrilateral is a parallelogram (6 ways to do so!)

A Study of all things 4 sided. Quadrilaterals Parallelograms.

Parallelograms Unit 8.2. What is a parallelogram Definition: a parallelogram is a quadrilateral with both pairs of opposite sides parallel.

What are the x- and y-intercepts of the function graphed at the right ? a. (0,2) and (0,3) b. (2,0) and (0,-3) c. (0,-2) and (3,0) d. (0,2) and (3,0) 5.1.

Parallelograms Chapter 5 Ms. Cuervo.

Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram.

What is a Parallelogram? A quadrilateral with both pairs of opposite sides parallel. Symbol for parallelogram: ___________ of parallelograms can serve.

6.3 Proving Quadrilaterals are Parallelograms Day 3.

6.3 Proving Quadrilaterals are Parallelograms Learning Target I can use prove that a quadrilateral is a parallelogram.

Class Opener 1/5/12 Use the properties of a kite to determine the value of each variable and each side length 3x - 4 x 2y - 5 Y + 1.

Chapter 8.2 Notes: Use Properties of Parallelograms

8.2 Parallelograms. Objectives  Recognize and apply properties of the sides and angles of parallelograms.  Recognize and apply properties of the diagonals.

Geometry 6-4 Properties of Rhombuses, Rectangles, and Squares.

EXAMPLE 3 List properties of special parallelograms

6.3 Proving Quadrilaterals are Parallelograms. Objectives: Prove that a quadrilateral is a parallelogram. Use coordinate geometry with parallelograms.

Rectangles Section 8-4. rectangle – a quadrilateral with 4 right angles Since a rectangle is a special type of parallelogram, it has all the properties.

A D B C Definition: Opposite Sides are parallel.

Chapter 6 Lesson 2 Objective: To use relationships among diagonals, angles and sides of parallelograms.

7.2 Parallelograms. Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Consecutive angles Opposite angles.

6-2 Properties of Parallelograms. Quadrilaterals In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side. – In.

Parallelograms Properties & Attributes. Parallelograms …are quadrilaterals in which both pairs of opposite sides are parallel If a quadrilateral is a.

Geometry Lesson 6 – 2 Parallelograms Objective: Recognize and apply properties of the sides of angles of parallelograms. Recognize and apply properties.

Interior and exterior angles. Exterior and interior angles are supplementary.

Sections  A parallelogram must have:  Both pair of opposite sides congruent  Both pair of opposite angles congruent  Consecutive angles that.

 Parallelograms are quadrilaterals, this means they have 4 sides.

Lesson 5-3 Theorems Involving Parallel Lines (page 177) Essential Question How can the properties of quadrilaterals be used to solve real life problems?

Warm-Up ABCD is a parallelogram. AB = 12 and BC = 25

Properties of Parallelograms

6-2 Properties of Parallelograms

6.2 Properties of Parallelograms

8.2 Parallelograms.

Parallelograms.

Section 6 – 2 Properties of Parallelograms

Chapter 5 -- Quadrilaterals

Ways to Prove Quadrilaterals are Parallelograms

Polygons – Parallelograms

Parallelograms Parallelogram - A quadrilateral with both pairs of opposite sides parallel. Theorem 8.3 Opposite sides of a parallelogram are congruent.

Properties of Parallelograms

6-2 Properties of Parallelograms

Properties of Parallelograms

Lesson 6-3 Rectangles Lesson 6-3: Rectangles.

6.2 Properties of Parallelograms

6.2 Properties of Parallelograms

Section 5-1 Parallelograms.

7.1 Properties of Parallelograms

Six Properties of Parallelograms

6.2 Properties of parallelograms

8.2 Use Properties of Parallelograms

Unit 6 Quadrilaterals Section 6.1 Properties of Parallelograms

Lesson 61 Determining if a Quadrilateral is a Parallelogram

6.3 Proving Quadrilaterals are Parallelograms

Properties of Parellograms

6-1 Parallelograms Objectives:

6.2 and 6.3: Quadrilaterals and Parallelograms

Module 15: Lesson 6 Properties of Parallelograms

6.3 Conditions for Parallelograms

6.2 Properties of Parallelograms

Proving Quadrilaterals Are Parallelograms

Properties of Parallelograms

6.3 Proving Quadrilaterals and Parallelograms

8.2 Parallelograms.

Properties of Parellograms

Bellringer Can a triangle have the sides with the given lengths? Explain 8mm, 6mm, 3mm 5ft, 20ft, 7ft 3m, 5m, 8m.

Presentation transcript:

6-2 Properties of Parallelograms

Area Area of Parallelogram A = base x height

Proof 2. 3. 4. 5. 6. 7. 8.

Proof 1. 2. 3. 4. 5. 6. 7.

Theorems Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Consecutive angles of a parallelogram are supplementary. Diagonals of a parallelogram bisect each other.

Theorems If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Examples 1) Find area of the parallelogram 2) Find area of a parallelogram with vertices (-5,-3), (-2,3), (2,3) & (-1,-3).

Examples 3) If AB=3x + 11, BC = 2x + 19 and CD = 7x – 17, find x. 4) If m<BAD = y and m<ADC = 4y – 70, find y. 5) If m<ABC=2x + 100 and m<ADC=6x + 84, find m<BCD.

Examples 6) If m<BCD=80 and m<CAD=34, find m<ACD. 7) If AP=3x, BP=y, CP=6x - 42, and DP=27 - 2y, find x &y.

Examples 8) Find EH.

Example: Honors Geometry Statements Reasons 1. 2. 3. 4. 5. 6.