Dapo Adegbile Brandon Abad Jude St. Jean Period:12

Slides:

Advertisements

Similar presentations

Our lesson Area Trapezoids Confidential.

Advertisements

Quadrilateral Proofs Page 4-5.

Parallelograms Quadrilaterals are four-sided polygons

8.3 Tests for Parallelograms

Row 1 Row 6 Row 5 Row 2 Row 7 Row 3 Row 8 Row 4 Row 9 Row 10 Row 11.

4.1 Quadrilaterals Quadrilateral Parallelogram Trapezoid

Lizzy Butler Kaitlyn Smeraldo Krisitn Donadio

8.6 Trapezoids.

Honors Geometry Section 4.5 (3) Trapezoids and Kites.

Trapezoids Jude Saint-Jean DapoBrandonPeriod:12. Definition A quadrilateral which has at least 1 pair of parallel sides A quadrilateral which has at least.

Sect. 6.5 Trapezoids and Kites Goal 1 Using Properties of Trapezoids Goal 2 Using Properties of Kites.

6-6 Trapezoids and Kites.

© 2010 Pearson Education, Inc. All rights reserved Constructions, Congruence, and Similarity Chapter 12.

Quadrilaterals Bryce Hall 4 Wennersten.

Warm up: Identify the best name for the given traits of each quadrilateral. 1.) ABCD has two sets of parallel sides and a right angle. 2.) HGDT has 2 sets.

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.

Chapter 5 Pre-AP Geometry

Similarity and Parallelograms.  Polygons whose corresponding side lengths are proportional and corresponding angles are congruent.

Geometry Notes Lesson 4.2A Properties of Special Quadrilaterals R.4.G.1 Explore and verify the properties of quadrilaterals.

Unit 8 Part 3 Properties of Quadrilaterals

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.

B D A C Conjecture: m  B = 2(m  A) 7.. A B C D E 30  x 1. From HW # 6 Given: x = 15 Find the measure of the angle marked x.

Section 16.1 Pythagorean Theorem a=11.6. x=3.86 y=4.60 x=

GEOMETRY REVIEW Look how far we have come already!

8.5 Trapezoids.

Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.

Proof Geometry.  All quadrilaterals have four sides.  They also have four angles.  The sum of the four angles totals 360°.  These properties are.

5.11 Use Properties of Trapezoids and Kites. Vocabulary  Trapezoid – a quadrilateral with exactly one pair of parallel sides. Base Base Angle Leg.

8.5 Trapezoids and Kites. Objectives: Use properties of trapezoids. Use properties of kites.

Trapezoids & Kites Sec 6.5 GOALS: To use properties of trapezoids and kites.

Geometry Section 6.5 Trapezoids and Kites. A trapezoid is a quadrilateral with exactly one pair of opposite sides parallel. The sides that are parallel.

Trapezoids April 29, 2008.

Using Coordinate Geometry to Prove Parallelograms

Parallelograms Quadrilaterals are four-sided polygons Parallelogram: is a quadrilateral with both pairs of opposite sides parallel.

A QUADRALATERAL WITH BOTH PAIRS OF OPPOSITE SIDES PARALLEL

Geometry 6-6 Trapezoids Only one pair of parallel sides (called bases) Non-parallel sides are called legs Base angles share a common base.

Special Quadrilaterals Properties of Kites & Trapezoids.

Lizzy Butler Kaitlyn Smeraldo Krisitn Donadio. Definitions Trapezoid: quadrilateral that has two parallel sides Isosceles Trapezoid: A quadrilateral with.

Trapezoids Euclidean Geometry High School Math Online.

Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 4.4 The Trapezoid.

Confidential1. 2 Find the area: 1. Base = 10 cm, height = 2 cm 2. Base = 6 m, height = 4 m Find the base of the triangle: 3. area = 96 cm 2, height =

Quadrilaterals Four sided polygons.

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

Using the Distance Formula in Coordinate Geometry Proofs.

Use Properties of Trapezoids and Kites Lesson 8.5.

8.3 Test for Parallelograms Check.3.2 Connect coordinate geometry to geometric figures in the plane (e.g. midpoints, distance formula, slope, and polygons).

Parallelograms Quadrilaterals are four-sided polygons Parallelogram: is a quadrilateral with both pairs of opposite sides parallel.

TRAPEZOIDS AND KITES Lesson 6-6. VOCABULARY: Trapezoid: A quadrilateral with exactly one pair of parallel sides. Bases: The parallel sides of a trapezoid.

TRAPEZOIDS / MIDSEGMENTS AND KITES Lesson 2 – 4 MATH III.

Aim: How can we solve coordinate quadrilateral proofs

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

Quadrilaterals.

Using Coordinate Geometry to Prove Parallelograms

Quadrilaterals and Coordinates Proof

Chapter 6 Review This is a review over all the stuff that you have learned, or should have learned, in chapter 6.

Chapter 7 Proofs and Conditional Probability

Using Coordinate Geometry to Prove Parallelograms

Trapezoid Special Notes!

Chapter 7 Proofs and Conditional Probability

Chapter 5: Quadrilaterals

12 Chapter Congruence, and Similarity with Constructions

My Favorite No!! D EB = 7 AE = 10 DE = DC Find AD E C B A.

What is a quadrilateral??

Lesson: 6.6 Trapezoids Objectives:

PROVING A QUADRILATERAL IS AN ISOSCELES TRAPEZOID

12 Chapter Congruence, and Similarity with Constructions

Proving a quadrilateral is a parallelogram

Using Coordinate algebra, definitions, and properties

Presentation transcript:

Dapo Adegbile Brandon Abad Jude St. Jean Period:12 Trapezoids Dapo Adegbile Brandon Abad Jude St. Jean Period:12

Definition A quadrilateral that has 1 pair of parallel sides A trapezoid with 1 pair of congruent sides

Properties of sides The bases (top and bottom) of an isosceles trapezoid are parallel. The legs of an isosceles trapezoid are congruent. The angles on either side of the bases are congruent. The bases (top and bottom) of a trapezoid are parallel. Unlike the Isosceles Trapezoid it does not need to have any congruent sides.

Properties of angles Adjacent angles along the sides are supplementary. Base angles of isosceles trapezoid are congruent. Normal trapezoids don’t have any special properties. All of the angles within a trapezoid add up to 360 degrees.

Proof Given: BC ll AD, AB = DC Prove: <1=<2 Given Construction Definition of a parallelogram Opposite sides of Parallelogram are congruent Transitive Property Isosceles Triangle Theorem (if sides than angles) Corresponding angles Transitive property Quad. ABCD is an Isosceles Trapezoid BC ll AD AB = DC Construct a line through C that is ll to AB AB ll EC Quad ABCE is a parallelogram AB = EC DC = CE <3 = <4 <1 = <3 <1 = <4

Properties of diagonals The diagonals of an isosceles triangle are congruent. Nothing special happens with the diagonals.

Proof Given Quad. PQRS is a trapezoid SR ll PQ SP=RQ Given: PQRS is an Isosceles Trapezoid SR ll PQ SP=RQ Prove: RP=SQ Given Definition of Trapezoid Reflexive Property CPCTC Quad. PQRS is a trapezoid SR ll PQ SP=RQ <SPQ=<RPQ PQ=PQ RP=SQ

Lines of symmetry A regular trapezoid has no lines of symmetry Isosceles trapezoids have only 1 line of symmetry

Coordinate Geometry http://mathopenref.com/coordtrapezoid.html

formulas Perimeter = a + b + c + B Area = 1/2h(B+b) Area of parallelogram (B+b) x h But, this is double of what we need. So, multiply by 1/2. The Area could also be altitude x median

Other facts Right Trapezoid- a trapezoid with 2 right angles median- is a line segment linking the midpoints of the two legs of the trapezoid To find the length of the median you can find the length of the base and divide it by 2 or find the distance between the 2 midpoints of the legs Altitude- is the perpendicular distance from one base to the other British call it Trapezium

Suggested Websites http://mathopenref.com/coordtrapezoid.html http://www.coolmath.com/reference/trapezoids.html http://www.cliffsnotes.com/study_guide/Properties-of-Trapezoids.topicArticleId-18851,articleId-18798.html