Lesson 6 CCSS G-C 3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a.

Slides:

Advertisements

Similar presentations

Introduction Construction methods can also be used to construct figures in a circle. One figure that can be inscribed in a circle is a hexagon. Hexagons.

Advertisements

Constructing Regular Hexagons Inscribed in Circles Adapted from Walch Education.

Adapted from Walch Education Triangles A triangle is a polygon with three sides and three angles. There are many types of triangles that can be constructed.

By Greg Wood. Introduction  Chapter 13 covers the theorems dealing with cyclic polygons, special line segments in triangles, and inscribed & circumscribed.

11.2a Area of Regular Polygons CCSSLESSON GOALS  Identify the radius, central angle, and apothem of a polygon.  Find the measure of a polygon’s central.

Proving Properties of Parallelograms

Introduction The ability to copy and bisect angles and segments, as well as construct perpendicular and parallel lines, allows you to construct a variety.

10.3 Inscribed Angles Goal 1: Use inscribed angles to solve problems Goal 2: Use properties of inscribed polygons CAS 4, 7, 16, 21.

Inscribed Angles Section 10.5.

Angles, Arcs, and Chords Advanced Geometry Circles Lesson 2.

Warm – up 2. Inscribed Angles Section 6.4 Standards MM2G3. Students will understand the properties of circles. b. Understand and use properties of central,

1 Sect Inscribed Angles Goal 1 Using Inscribed Angles Goal 2 Using Properties of Inscribed Angles.

Section 10.3 – Inscribed Angles

Geometry Section 10-4 Use Inscribed Angles and Polygons.

Chapter 10.4 Notes: Use Inscribed Angles and Polygons

Introduction Circles have several special properties, conjectures, postulates, and theorems associated with them. This lesson focuses on the relationship.

Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

Inscribed Angles 10.3 California State Standards

Lesson 9.3A R.4.G.6 Solve problems using inscribed and circumscribed figures.

Geometer Sketch Pad Assignment Mark Breakdown. Exercise #1 – Question #1 Medians 4 All three meet at one point 4 Circle with a center at the centroid.

Circles. Points & Circle Relationships Inside the circle THE circle Outside the circle A C B E G F D.

6.3 – 6.4 Properties of Chords and Inscribed Angles.

Have your homework out and be ready to discuss any questions you had. Wednesday, February 6, 2013 Agenda No TISK or MM HW Questions (9-2 & 9-3) Lesson.

Objective: Find the area of trapezoids and kites. Warm up Find the area. a. b.

Cyclic quadrilateral Class IX Prepared by P.E.Venugopalan K.V.KELTRON NAGAR.

21C: Cyclic quadrilaterals. What is a cyclic quadrilateral?  A cyclic quadrilateral is a 4 sided shape that has all four corners on the circumference.

Bisectors in Triangles Chapter 5 Section 3. Objective Students will identify properties of perpendicular bisectors and angle bisectors.

CIRCLES 1 Moody Mathematics. VOCABULARY: Identify the name of the object pictured in each frame. VOCABULARY: Identify the name of the object pictured.

Geometry: From Triangles to Quadrilaterals and Polygons.

Inscribed and Circumscribed Polygons Inscribed n If all of the vertices of a polygon lie on the circle, then the polygon is inscribed.

Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

10.3 Inscribed Angles Intercepted arc. Definition of Inscribed Angles An Inscribed angle is an angle with its vertex on the circle.

Section 10-3 Inscribed Angles. Inscribed angles An angle whose vertex is on a circle and whose sides contain chords of the circle. A B D is an inscribed.

Use Inscribed Angles and Polygons Lesson Definitions/Theorem 10.7 BAC = ½(BC) Intercepted Arc Inscribed Angle A B C. Central Angle.

Inscribed Angles Lesson 10.3b California State Standards 4: Prove theorems involving congruence and similarity 7: Prove/use theorems involving circles.

Chapter 5 Lesson 3 Objective: Objective: To identify properties of perpendicular and angle bisectors.

Topic 12-3 Definition Secant – a line that intersects a circle in two points.

Lesson 11-4 Areas of Regular Polygons (page 440) Essential Question How can you calculate the area of any figure?

Chapter 3 Using tools of Geometry. Lesson 3.1 Sketch – a drawing made free hand, no tools Draw – a drawing made with the tools. Compass and Straightedge.

Date: 8.1 Notes: Polygon Interior Angles Sum Lesson Objective: Find and use the sum of the measures of the interior angles of a polygon. CCSS: G.MG.1.

Day 43 – regular hexagon inscribed in a circle

Day 44 – Summary of inscribed figures

Bisectors of Triangles

Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

Introduction Triangles are not the only figures that can be inscribed in a circle. It is also possible to inscribe other figures, such as squares. The.

Tangent Lines Geometry 11-1.

Day 41 – Equilateral triangle inscribed in a circle

Constructing Squares Inscribed in Circles

straight and curved lines

10.7 Inscribed and Circumscribed Polygons

Learning Targets I will be able to: Prove and apply properties of perpendicular bisectors of a triangle. and prove and apply properties of angle bisectors.

Introduction Circles have several special properties, conjectures, postulates, and theorems associated with them. This lesson focuses on the relationship.

Lesson: 10 – 1 Circles and Circumference

Investigating Inscribed Angles on Diameters

Lesson 2 CCSS Identify and describe relationships among inscribe angles, radii and chords. Include the relationship between central, inscribed, and circumscribed.

Unit 4: Circles and Volume

8.3 Inscribed Polygons There are a couple very helpful Theorems about Polygons Inscribed within circles that we will look at.

WELCOME Math 2 Last Night’s HW: None Chapter 9: Circles

Section 10.3 – Inscribed Angles

5.3 Congruent Triangles & Proof

Bisectors of a Triangle

Day 44 – Summary of inscribed figures

Day 126 – Inscribed and circumscribed circles of a triangle

Section 10.4 Use Inscribed Angles And Polygons Standard:

10.4 Inscribed Angles.

What are the main properties of Trapezoids and Kites?

Bisectors of a Triangle

Presentation transcript:

Lesson 6 CCSS G-C 3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Investigating Inscribed Quadrilaterals Draw a circle. Draw an inscribed quadrilateral. Make sure all 4 vertices of the quadrilateral lie on the circle. Label the vertices A, B, C, and D. Using a protractor measure the four angles of the quadrilateral to the nearest degree.

Use a compass to draw a circle with a diameter greater than the circle in Step A. Plot points E, F, G, and H consecutively around the circumference of the circle so that the center of the circle is not inside quadrilateral EFGH. Use a straightedge to connect each pair of consecutive points to draw quadrilateral EFGH.

Proving the Inscribed Quadrilateral Theorem

Assignments