BY: MARIANA BELTRANENA 9-5 POLYGONS AND QUADRILATERALS.

Slides:

Advertisements

Similar presentations

Journal 6 By: Mariana Botran.

Advertisements

Quadrilateral Venn Diagram

Unit 3– Quadrilaterals Review for Final Exam.

Chapter 6.1 Common Core G.DRT.5 – Use Congruence…criteria to solve problems and prove relationships in geometric figures. Objectives – To find the sum.

Geometry BINGO Chapter 6 Test Review.

6-6 Trapezoids and Kites.

Advanced Geometry 5.4 / 5 Four Sided Polygons /    Properties of Quadrilaterals Learner Objective: I will solve problems using properties   of special.

Jose Pablo Reyes. Polygon: Any plane figure with 3 o more sides Parts of a polygon: side – one of the segments that is part of the polygon Diagonal –

Quadrilateral Proofs.

Journal 6 By: Maria Jose Diaz-Duran. Describe what a polygon is. Include a discussion about the parts of a polygon. Also compare and contrast a convex.

Polygons and Quadrilaterals

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

Chapter 6 Quadrilaterals.

Quadrilaterals Chapter 8.

Bellwork  Solve for x x-2 5x-13 No Clickers. Bellwork Solution  Solve for x x-2 5x-13.

Javier Mendez. A polygon is any shape that is closed, has more than two sides and it does not have curved sides. In a polygon, the segments cannot intersect.

Chapter 6: Quadrilaterals

Polygon Properties - Ch 5 Quadrilateral Sum Conjecture The sum of the measures of the four angles of any quadrilateral is… degrees. C-30 p. 256.

Name That Quadrilateral  Be as specific as possible.  Trapezoid.

Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c √3.

Chapter 6 Quadrilaterals. Section 6.1 Polygons Polygon A polygon is formed by three or more segments called sides –No two sides with a common endpoint.

Geometry--Ch. 6 Review Classify each polygon as regular/irregular, concave/convex, and name it based on its number of sides: 1)2) irregular concave decagon.

A polygon is any closed shape with straight edges, or sides. Side: a segment that forms a polygon Vertex: common endpoint of sides. Diagonal: segment.

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.

 Parallelograms Parallelograms  Rectangles Rectangles  Rhombi Rhombi  Squares Squares  Trapezoids Trapezoids  Kites Kites.

Final Exam Review Chapter 8 - Quadrilaterals Geometry Ms. Rinaldi.

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.

6-6 Trapezoids and Kites Objective: To verify and use properties of trapezoids and kites.

Special Quadrilaterals

Aim: what are the properties of quadrilaterals? Do Now: Name 2 ways to identify a parallelogram as a square 1.A rectangle with 1 pair of consecutive congruent.

A QUADRALATERAL WITH BOTH PAIRS OF OPPOSITE SIDES PARALLEL

Chapter 6.1 Notes Polygon – is a simple, closed figure made with straight lines. vertex vertex side side Convex – has no indentation Concave – has an indentation.

Objectives To identify any quadrilateral, by name, as specifically as you can, based on its characteristics.

Please click the speaker symbol on the left to hear the audio that accompanies some of the slides in this presentation. Quadrilaterals.

Midsegments of a Triangle

Obj: SWBAT identify and classify quadrilaterals and their properties

PROPERTIES AND ATTRIBUTES OF POLYGONS

Geometry SECTION 6: QUADRILATERALS. Properties of Parallelograms.

Unit 7 Quadrilaterals. Polygons Polygon A polygon is formed by three or more segments called sides –No two sides with a common endpoint are collinear.

5.5 Indirect Reasoning -Indirect Reasoning: All possibilities are considered and then all but one are proved false -Indirect proof: state an assumption.

Quadrilaterals Four sided polygons.

By: Gabriel Morales Journal Chapter 6. 3 I want Corrected (0-10 pts.) Describe what a polygon is. Include a discussion about the parts of a polygon. Also.

Always, Sometimes, or Never

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

5.4 Quadrilaterals Objectives: Review the properties of quadrilaterals.

Chapter 6: Quadrilaterals Fall 2008 Geometry. 6.1 Polygons A polygon is a closed plane figure that is formed by three or more segments called sides, such.

 Parallelograms Parallelograms  Rectangles Rectangles  Rhombi Rhombi  Squares Squares  Trapezoids Trapezoids  Kites Kites.

Chapter 6, Section 1 Polygons. Describing a Polygon An enclosed figure (all segments) Two segments a point called a vertex Each segment is called.

Journal 6 Cristian Brenner. Polygons A polygon is a close figuire with straight sides that the line dont interset each other. With three or more segments.

Quadrilateral Foldable!

7/1/ : Properties of Quadrilaterals Objectives: a. Define quadrilateral, parallelogram, rhombus, rectangle, square and trapezoid. b. Identify the.

A polygon that is equilateral and equiangular. Regular polygon.

Journal 6: Polygons Delia Coloma 9-5.

Chapter 7 Review.

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

POLYGONS ( except Triangles)

Chapter 6.1 Notes Polygon – is a simple, closed figure made with straight lines. vertex vertex side side Convex – has no.

Math Journal 6.

Polygons and Quadrilaterals

BY: Amani Mubarak 9-5 Journal chapter 6.

Geometry Quick Discussion 10.1 Squares and Rectangles

6.1 The Polygon angle-sum theorems

U1 Day 12 - Properties of Parallelograms

U1 Day 11 - Properties of Parallelograms

6.4 Rhombuses, Rectangles, and Squares 6.5 Trapezoids and Kites

Fill in the following table – checking each characteristic that applies to the figures listed across the top; Characteristic Polygon Quadrilateral Parallelogram.

Y. Davis Geometry Notes Chapter 6.

Presentation transcript:

BY: MARIANA BELTRANENA 9-5 POLYGONS AND QUADRILATERALS

Polygon A polygon is a closed figure with more than 3 straight sides which end points of two lines is the vertex.

Parts of Polygons Sides- each segment that forms a polygon Vertex- common end point of two sides. Diagonal- segments that connects any two non consecutive vertices.

Convex and Concave polygons Concave- any figure that has one of the vertices caved in. Convex- any figure that has all of the vertices pointing out.

Equilateral and Equiangular Equilateral- all sides are congruent. Equiangular- all angles are congruent.

Interior Angles Theorem for Polygons The sum of the interior angles of a polygon equals the number of the sides minus 2, times 180. (n- 2)180. For each interior angle it is the same equation divided by the number of sides.

examples Find the sum of the interior angle measure of a convex octagon and find each interior angle.  (n-2)180  (8-2)180= 1,080. The interior angles measure 1,080 degrees.  1080/8=135. Each interior angle measures 135 degrees. Find the sum of the interior angle measure of a convex doda-gon and find each interior angle.  (12-2)180= 1,800  interior measure  1,800/12=  each interior measure

Find each interior measure. (4-2)180=360 c + 3c + c + 3c = 360 8c=360 C= 45 Plug in c m<P = m<R = 45 degrees m<Q= m<S = 135 degrees.

Theorems of Parallelograms and its converse if a quadrilateral is a polygon then the opposite sides are congruent.

examples

Converse: if both pairs of opposite sides are congruent then the quadrilateral is a polygon EXAMPL ES

Theorems of Parallelograms and its converse If a quadrilateral has one set of opposite congruent and parallel sides then it is a parallelogram.

This quad. Is a parallelogram because it has one pair of opposite sides congruent and one pair of parallel sides. This figure is also a parallelogram because it has two pairs of parallel and congruent opposite sides.

Converse: If one pair of opposite sides of a quadrilateral are parallel and congruent, then it is a parallelogram Examples: Given- KL ll MJ, KL congruent to MJ Prove- JKLM is a parallelogram Proof: It is given that KL congruent to MJ. Since KL ll MJ, <1 congruent to <2 by the alternate interior angles theo. By the reflexive property of congruence, JL congruent JL. So triangle LMJ by SAS. By CPCTC, <3 congruent <4 and JK ll to LM by the converse of the alternate interior angles theo. Since the opposite sides of JKLM are parallel, JKLM is a parallelogram by deff.

Define if the quadrilateral must be a parallelogram. Yes it must be a parallelogram because if one pair of opposite sides of a quadrilateral are parallel and congruent, then it is a parallelogram.

Theorems of Parallelograms and its converse If a quadrilateral has consecutive angles which are supplementary, then it is a parallelogram

Converse: If a quadrilateral is supplementary to both of its consecutive angles, then it is a parallelogram.

Theorems of Parallelograms and its converse If a quadrilateral is a polygon then the opposite angles are congruent.

Converse: If both pair of opposite angles are congruent then the quadrilateral is a parallelogram.

How to prove a Quadrilateral is a parallelogram. opposite sides are always congruent opposite angles are congruent consecutive angles are supplementary diagonals bisect each other has to be a quadrilateral and sides parallel one set of congruent and parallel sides

Square Is a parallelogram that is both a rectangle and a square.  Properties of a square:  4 congruent sides and angles  Diagonals are congruent.

rhombus Is a parallelogram with 4 congruent sides  Properties  Diagonals are perpendicular

rectangle Is any parallelogram with 4 right angles. Theorem: if a a quadrilateral is a rectangle then it is a parallelogram.  Properties  Diagonals are congruent  4 right angles.

Comparing and contrasting

Trapezoids Is a quadrilateral with one pair of sides parallel and the other pair concave. There are isosceles trapezoids with the two legs congruent to each other. Diagonals are congruent. Base angles are congruent.

Trapezoid theorems Theorems:  6-6-3: if a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.  6-6-4: a trapezoid has a pair of congruent base angles, then the trapezoid is isosceles.  6-6-5: a trapezoid is isosceles if and only if its diagonals are congruent.

Trapezoid midsegment theorem: the midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the lengths of the bases.

Kites A kite has two pairs of adjacent angles Diagonals are perpendicular One of the diagonals bisect each other.

Kite theorems 6-6-1: if a quad. is a kite, then its diagonals are perpen 6-6-2: if a quad is a kite, then exactly one pair of opposite angles are congruent.