Introduction One of the most famous drawings of all time is Leonardo da Vinci’s Vitruvian Man. Da Vinci’s sketch was of a man enclosed by a circle that.

Slides:

Advertisements

Similar presentations

6.3/4 Rhombuses, Rectangles, and Squares. Three Definitions 1.A rhombus is a parallelogram with four congruent sides. 1.A rectangle is a parallelogram.

Advertisements

CIRCLES 2 Moody Mathematics.

Angles in a Circle Keystone Geometry

Introduction What does it mean to be opposite? What does it mean to be consecutive? Think about a rectangular room. If you put your back against one corner.

1 Lesson 6.3 Inscribed Angles and their Intercepted Arcs Goal 1 Using Inscribed Angles Goal 2 Using Properties of Inscribed Angles.

Introduction In the third century B. C., Greek mathematician Euclid, often referred to as the “Father of Geometry,” created what is known as Euclidean.

Introduction There are many kinds of quadrilaterals. Some quadrilaterals are parallelograms; some are not. For example, trapezoids and kites are special.

For each circle C, find the value of x. Assume that segments that appear to be tangent are tangent. 1)2)

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

6.4 Use Inscribed Angles and Polygons Quiz: Friday.

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.

11-3 Inscribed Angles Objective: To find the measure of an inscribed angle.

Chapter 12.3 Inscribed Angles

Geometry Section 10-4 Use Inscribed Angles and Polygons.

Warm-Up Find the area of the shaded region. 10m 140°

Section 9.5 INSCRIBED ANGLES. Inscribed Angle What does inscribe mean? An inscribed angle is an angle whose vertex is on a circle and whose sides contain.

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

Bell work 1 Find the measure of Arc ABC, if Arc AB = 3x, Arc BC = (x + 80º), and __ __ AB BC AB  BC AB = 3x º A B C BC = ( x + 80 º )

Lesson 8-5: Angle Formulas 1 Bell Ringer 5/27/2010 Find the value of x.

11.3 Inscribed angles By: Mauro and Pato.

12.3 Inscribed Angles An angle whose vertex is on the circle and whose sides are chords of the circle is an inscribed angle. An arc with endpoints on the.

Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle.

Inscribed Angles Section 9-5. Inscribed Angles An angle whose vertex is on a circle and whose sides contain chords of the circle.

9-4 Inscribed Angles Objectives: To recognize and find measures of inscribed angles. To find properties of inscribed angles.

Inscribed angles [11.3] Objectives Students will be able to… Find the measure of an inscribed angle Find the measures of an angle formed by a tangent and.

11.3: INSCRIBED ANGLES Objectives: Students will be able to… Apply the relationship between an inscribed angle and the arc it intercepts Find the measures.

Inscribed Angles Inscribed angles have a vertex on the circle and sides contain chords of the circle.

Section 9-5 Inscribed Angles. Inscribed angles An angle whose vertex is on a circle and whose sides contain chords of the circle. A B C D are inscribed.

Lesson 7.4. Conjectures Geo Sketchpad C-68 The measure of an inscribed angle in a circle is half the measure of the arc it intercepts.

Geometry 10.4 Inscribed Angles. Vocabulary Inscribed Angle Intercepted Arc B A C.

10.4 Inscribed Angles. Open a new geogebra file 1)Construct a circle A. 2)Place a point C on the circle such that arc BC is a minor arc. 3)Find the measure.

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

Proving Properties of Inscribed Quadrilaterals Adapted from Walch Education.

 Copy thm 12.9, corollaries, and thm from pgs 679 and 680.

Friday-Chapter 6 Quiz 2 on

Objective: Measures of Inscribed Angles & Inscribed Polygons. (3.12.3) Section 10.4.

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

Warm-up Find the measure of each arc.. Inscribed Angles.

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

Inscribed Angles December 3, What is an inscribed angle? An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords.

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.

Geometry Section 10.3 Inscribed Angles. Recall that a *central angle is an angle What is the relationship between a central angle and the are that it.

PROPERTIES OF CIRCLES Chapter – Use Properties of Tangents Circle Set of all points in a plan that are equidistant from a given point called.

GEOMETRY INSCRIBED ANGLES Unit 6-2. Central angles A __________ ____________ is an angle whose vertex is at the center of a circle with sides that are.

Circle Unit Part 4 Angles

Geometry 11-4 Inscribed Angles

Inscribed Angles Geometry 11-3.

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

Inscribed Angles and their Intercepted Arcs

Lesson 15.2 Materials: Notes Textbook.

Introduction One of the most famous drawings of all time is Leonardo da Vinci’s Vitruvian Man. Da Vinci’s sketch was of a man enclosed by a circle that.

11-3 Inscribed Angles Theorems: Inscribed Angle Theorem, 11-10

Geometry 9.5 Inscribed Angles.

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

Inscribed Angles and Quadrilaterals

Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle

9-5 Inscribed Angles.

_____________: An angle whose vertex is on the circle and whose sides are chords of the circle

Arcs and Angles Relationships between Arcs and Angles

Circles and inscribed angles

Section 10.4 Use Inscribed Angles And Polygons Standard:

Inscribed Angles & Inscribed Quadrilaterals

10.4 Inscribed Angles.

Presentation transcript:

Introduction One of the most famous drawings of all time is Leonardo da Vinci’s Vitruvian Man. Da Vinci’s sketch was of a man enclosed by a circle that touched the man’s feet and hands. In this lesson, we will investigate the properties of quadrilaterals inscribed in a circle : Proving Properties of Inscribed Quadrilaterals

Key Concepts An inscribed quadrilateral is a quadrilateral whose vertices are on a circle. The opposite angles of an inscribed quadrilateral are supplementary. m ∠ A + m ∠ C = 180 m ∠ B + m ∠ D = : Proving Properties of Inscribed Quadrilaterals

Key Concepts Remember that the measure of an inscribed angle is half the measure of the intercepted arc. Rectangles and squares can always be inscribed within a circle : Proving Properties of Inscribed Quadrilaterals

Common Errors/Misconceptions mistakenly thinking that the diagonal of any inscribed quadrilateral is a diameter of the circle : Proving Properties of Inscribed Quadrilaterals

Guided Practice Example 1 Consider the inscribed quadrilateral in the diagram at right. What are the relationships between the measures of the angles of an inscribed quadrilateral? : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 1, continued 1.Find the measure of ∠ B. ∠ B is an inscribed angle. Therefore, its measure will be equal to half the measure of the intercepted arc. The intercepted arc has a measure of , or 174°. The measure of ∠ B is of 174, or 87° : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 1, continued 2.Find the measure of ∠ D. The intercepted arc has a measure of , or 186°. The measure of ∠ D is of 186, or 93° : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 1, continued 3.What is the relationship between ∠ B and ∠ D? Since the sum of the measures of ∠ B and ∠ D equals 180°, ∠ B and ∠ D are supplementary angles : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 1, continued 4.Does this same relationship exist between ∠ A and ∠ C ? The intercepted arc has a measure of , or 156°. The measure of ∠ A is of 156, or 78°. The intercepted arc has a measure of , or 204°. The measure of ∠ C is of 204, or 102°. The sum of the measures of ∠ A and ∠ C also equals 180°; therefore, ∠ A and ∠ C are supplementary : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 1, continued 5.State your conclusion. The opposite angles of an inscribed quadrilateral are supplementary : Proving Properties of Inscribed Quadrilaterals ✔

Guided Practice: Example 1, continued : Proving Properties of Inscribed Quadrilaterals

Guided Practice Example 2 Consider the inscribed quadrilateral to the right. Do the relationships discovered between the angles in Example 1 still hold for the angles in this quadrilateral? : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 2, continued 1.Calculate the measures of all four angles of quadrilateral ABCE. ∠ A intercepts, so the measure of ∠ A is half the measure of : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 2, continued ∠ B intercepts, so the measure of ∠ B is half the measure of. ∠ C intercepts, so the measure of ∠ C is half the measure of : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 2, continued ∠ E intercepts, so the measure of ∠ E is half the measure of : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 2, continued 2.Find the sum of the measures of ∠ A and ∠ C. The sum of the measures of ∠ A and ∠ C is equal to = : Proving Properties of Inscribed Quadrilaterals

Guided Practice: Example 2, continued 3.State your conclusion. The measures of ∠ A and ∠ C sum to 180°, as do the measures of ∠ B and ∠ E ; therefore, it is still true that opposite angles of an inscribed quadrilateral are supplementary : Proving Properties of Inscribed Quadrilaterals ✔

Guided Practice: Example 2, continued : Proving Properties of Inscribed Quadrilaterals