1 Section 9: Rhombuses, Rectangles, and Squares. 2 Goals Use properties of diagonals of rhombuses, rectangles, and squares Use properties of sides and.

Slides:

Advertisements

Similar presentations

Math 310 Section 10 Quadrilaterals Review. Trapezoid Definition: A quadrilateral with a pair of parallel sides. Special Notes! All the properties of a.

Advertisements

5.7 Proving That Figures Are Special Quadrilaterals

Special Quadrilaterals

Rhombus and Square.

In this chapter you will learn about the special properties of quadrilaterals as well as find their perimeters and areas. You will explore the relationships.

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Slope and Distance Trapezoids What.

Quadrilaterals.

Direct Analytic Proofs. If you are asked to prove Suggestions of how to do this Two lines parallel Use the slope formula twice. Determine that the slopes.

6.6 Special Quadrilaterals. Example Quad ABCD has at least one pair of opp sides  What kinds of quads could it be? Parallelogram Rhombus Rectangle Square.

The Distance Formula Used to find the distance between two points: A( x1, y1) and B(x2, y2) You also could just plot the points and use the Pythagorean.

Properties of Other Quadrilaterals Students will be able to… Identify and use the properties of rectangles, squares, rhombuses, kites, and trapezoids.

1. Given Triangle ABC with vertices A(0,0), B(4,8), and C(6,2).

Review & Trapezoids. Properties of a Parallelogram A BC D 1. Opposite sides are parallel. 2 Opposite sides are congruent. 3. Opposite angles are congruent.

Kite, special member of Quadrilateral family. Family of Quadrilaterals.

For each, attempt to create a counter example or find the shape is MUST be….. Quadrilateral Properties.

INTERIOR ANGLES THEOREM FOR QUADRILATERALS By: Katerina Palacios 10-1 T2 Geometry.

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

Proving Properties of Special Quadrilaterals

6.4 Rhombuses, Rectangles, and Squares Day 4 Review  Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 °

Warm-Up ABCD is a parallelogram. Find the length of BC. A B C D 5x + 3 3x + 11.

Using Coordinate Geometry to Prove Parallelograms

2/9/15 Unit 8 Polygons and Quadrilaterals Special Parallelograms

Bell Ringer Lesson 6-4: Rhombus & Square 1. 2 Rhombi Rectangles & Squares.

6.4 Properties of Rhombuses, Rectangles, and Squares A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right.

Homework: Quadrilaterals & Coordinate Geometry Day 1 Wkst

Parallelograms have Properties Click to view What is a parallelogram? A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Rhombi & Squares Section 8-5. rhombus – a quadrilateral with 4 congruent sides Since a rhombus is a parallelogram, it has all the properties of a parallelogram.

Rhombuses, Rectangles, and Squares

Special Parallelograms

CHAPTER 5: QUADRILATERALS

SPECIAL TYPE OF PARALLELOGRAM 6.5 SQUARES. A quadrilateral with 4 congruent sides Characteristics of a square: Both sets of opp. sides are congruent and.

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

Proofs with Quadrilaterals. Proving Quadrilaterals are Parallelograms Show that opposite sides are parallel by same slope. Show that both pairs of opposite.

 Rhombus – a parallelogram with four congruent sides.  Rectangle – a parallelogram with four right angles.

6-4 Properties of Rhombuses, Rectangles, and Squares

Objectives: 1) To define and classify special types of quadrilaterals.

Pre-Requisite Information Pre-Calculus Day 1. Standard Form Ax + By= C NO FRACTIONS A cannot be negative Slope is –A/B Parallel Lines Perpendicular Lines.

6-4 Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares Lesson 8.4.

Geometry1 Section 6-4: Rhombuses, Rectangles, and Squares.

Proving Properties of Triangles and Quadrilaterals

Geometry SECTION 6: QUADRILATERALS. Properties of Parallelograms.

Lesson 6-4: Rhombus & Square

Copy this into your SOL Binder (day 49) If your are interested…..

Geometry Section 6.3 Conditions for Special Quadrilaterals.

Special Quadrilaterals. KITE  Exactly 2 distinct pairs of adjacent congruent sides  Diagonals are perpendicular  Angles a are congruent.

7.4 Properties of Special Parallelograms OBJ: Students will be able to use properties of special parallelograms and diagonals of special parallelograms.

Quadrilaterals Graphic Organizers.

Geometry Math 2. Proofs Lines and Angles Proofs.

Parallelogram Rectangle Rhombus Square Trapezoid Kite

Quadrilaterals and Polygons SOL Review Session. Names of Polygons Number of SidesName

Quadrilaterals Four sided polygons Non-examples Examples.

Do-Now 1)Find x. 2) Find x. 4x + 1 3x + 1 2x x 2x – 10 x 2 – 2x – 69.

G-05 “I can use coordinates to prove and apply properties of parallelograms.” Parallelogram, rectangle, rhombus and squares.

Warm Up:  Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving?  What is the measure of CD? 

Do Now: List all you know about the following parallelograms.

Properties of Parallelograms

Section 6.7: Areas of Triangles and Quadrilaterals

Using Coordinate Geometry to Prove Parallelograms

Using Coordinate Geometry to Prove Parallelograms

6-4: Properties of Special Parallelograms

Parallelogram Rectangle Rhombus Square Trapezoid Kite

8.4 Properties of Rhombuses, Rectangles, and Squares

6-5: Conditions of Special Parallelograms

Unit 6 Quadrilaterals Section 6.5 Properties of Rhombi and Squares

What is a quadrilateral??

Go over the Test.

Presentation transcript:

1 Section 9: Rhombuses, Rectangles, and Squares

2 Goals Use properties of diagonals of rhombuses, rectangles, and squares Use properties of sides and angles of rhombuses, rectangles, and squares Anchors Apply appropriate techniques, tools, and formulas to determine measurements. Analyze characteristics and properties of two and three dimensional geometric shapes and demonstrate understanding of geometric relationships.

3 Properties of Special Parallelograms Rhombus All the properties of a parallelogram All four sides are congruent The diagonals are perpendicular The diagonals bisect the interior angles 90  x x x x y y y y

4 All the properties of a parallelogram All sides meet at 90  Each of the diagonals are congruent Properties of Special Parallelograms Rectangle AB CD EAC = BD Makes two pairs of isosceles triangles. AE = EC = ED = EB xx xx y y y y

5 Properties of Special Parallelograms Square All the properties of a parallelogram All the properties of a rhombus All the properties of a rectangle AB CD 45  90 

6 Parallelogram RectanglesSquaresRhombuses

7 Rectangle ABCD  ABE = 10x - 5  BCA = 4x – 3 Find all angles.  ABE +  BCA = 90  X = 7 25  65  130  50  10x x - 3 = 90 

8 Rectangle QRST  QRU = 4x + 4  RUQ = 15x - 12 Find all angles.  QRU +  RQU +  RUQ = 180  X = 8 4x x x - 12 = 180  36  54  108  72 

9 Rhombus PROD  PRU = 9x - 4  PDU = 5x + 20 Find all angles.  PRU =  PDU 9x - 4 = 5x + 20 x = 6 90  50  40 

10 Rhombus JELY  UEJ = 2x + 6  YLU = 4x Find all angles.  UEJ +  YLU = 90  x =  2x x = 90  34  56  90 

11 What special type of quadrilateral is ABCD? A ( -4, 7 ), B ( 6, 9 ), C ( 8, 16 ) D ( -2, 14 ) Slope of AB = Slope of BC = Slope of CD = Slope of AD = 1 / 5 7 / 2 1 / 5 7 / 2 Length of AB = Length of BC = Length of CD = Length of AD = 2√26 √53 2√26 √53 ABCD is a parallelogram – b/c it has two sets of parallel and congruent sides. How do we do that? What do we need to know?

12 What special type of quadrilateral is EFGH? E ( 4, -8 ), F ( 7, -3 ), G ( 12, -6 ) H ( 9, -11 ) Slope of EF = Slope of FG = Slope of GH = Slope of EH = 5 / 3 -3 / 5 5 / 3 -3 / 5 Length of AB = Length of BC = Length of CD = Length of AD = √34 EFGH is a square – b/c it has two sets of parallel sides, all sides are congruent, and the slopes are negative reciprocals. How do we do that? What do we need to know?

13 What special type of quadrilateral is IJKL? I ( -9, -9 ), J ( -6, -2 ), K ( -3, -9 ) L ( -6, -16 ) Slope of IJ = Slope of JK = Slope of KL = Slope of IL = 7 / 3 -7 / 3 7 / 3 -7 / 3 Length of IJ = Length of JK = Length of KL = Length of IL = √58 IJKL is a rhombus– b/c it has two sets of parallel sides and all sides are congruent, How do we do that? What do we need to know? Diagonals are perpendicular. Slope of IK = 0 and slope of JL is undefined.

14 What special type of quadrilateral is MNOP? M ( 2, 2 ), N ( 5, 11 ), O ( 14, 14 ) P ( 11, 5 ) Slope of MN = Slope of NO = Slope of OP = Slope of MP = 3 1 / / 3 Length of MN = Length of NO = Length of OP = Length of MP = 3√10 MNOP is a rhombus– b/c it has two sets of parallel sides and all sides are congruent, How do we do that? What do we need to know? Diagonals are perpendicular. Slope of MO = 1 and slope of NP = -1.