warm up. p a b case i: central angle: vertex is at the center

Warm up

Upload: janis-cunningham

Post on 29-Dec-2015

223 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

Warm up

Central ANGLE = ARC

Case I: Central Angle: Vertex is AT the center

Case II: Inscribed Angle: Vertex is ON circle

ANGLE = ARC

2ANGLE

ARCANGLE

ARC

Page 4: Warm up. P A B Case I: Central Angle: Vertex is AT the center

Intercepted Arc:

• An arc whose endpoints are the two points of intersection of an angle with the circle and all points that lie within the angle.

Page 5: Warm up. P A B Case I: Central Angle: Vertex is AT the center

ArcdIntercepteAngleInscribed

160

The arc is twice as big as the angle!!

Page 6: Warm up. P A B Case I: Central Angle: Vertex is AT the center

120

Find the value of x and y

Page 7: Warm up. P A B Case I: Central Angle: Vertex is AT the center

Examples1. If mJK = 80 and JMK = 2x – 4, find x.

2. If mMKS = 56, find m MS.

x = 22

112

Page 8: Warm up. P A B Case I: Central Angle: Vertex is AT the center

72˚

If two inscribed angles intercept the same arc, then they are congruent.

Find the measure of DOG and DIG D

Page 9: Warm up. P A B Case I: Central Angle: Vertex is AT the center

If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

Page 10: Warm up. P A B Case I: Central Angle: Vertex is AT the center

Circumscribed Circle• The circumscribed circle (or

circumcircle) of a polygon is a circle which passes through all the vertices of the polygon.

• The center of this circle is called the circumcenter and its radius is called the circumradius.

Page 11: Warm up. P A B Case I: Central Angle: Vertex is AT the center

a quadrilateral inscribed in a circle: opposite angles are

supplementary.A B

180 CmAm180 DmBm

Page 12: Warm up. P A B Case I: Central Angle: Vertex is AT the center

If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.

diameter

Page 13: Warm up. P A B Case I: Central Angle: Vertex is AT the center

Example 3

In J, m3 = 5x and m 4 = 2x + 9.Find the value of x.

x = 3

Page 14: Warm up. P A B Case I: Central Angle: Vertex is AT the center

4x – 14 = 90

Example 4

In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.

x = 26

Bonus: What type of triangle is this? Why?

Page 15: Warm up. P A B Case I: Central Angle: Vertex is AT the center

110

110 + y =180y = 70

z + 85 = 180z = 95

Example 5 Find y and z.

Effect of Vertex Angle on Elastic-Plastic Stability of a

Holt Geometry 8-1 Find Angle Measures In Polygons 8-1 Find Angle Measures in Polygons Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation

02941 Physically Based Rendering - courses.compute.dtu.dk · • How do we make the object smooth? Interpolated per-vertex lighting? • What is the normal in a vertex? The angle-weighted

ANGULAR MEASUREMENT Angle: In Geometry an angle is the figure formed by two rays sharing a common end point, called the vertex of the angle. The magnitude

Geometry in Nature. This is an acute angle that has two line segments that meet at a vertex.acute angle Vertex

132A Angles & Angle Measures - Mrs. Nelson · 2018-09-06 · Standard Position: An angle with vertex (0, 0) and initial side on the xaxis. ... 132A Angles & Angle Measures previous

Warm-up: Find the six trig ratios for a –240˚ angle

By: Kandinsky€¦ · Kandinsky. Types of Angles. Vertex: Point B Ray: BA Ray: BC. straight angle acute angle obtuse angle 90' < v < 1800 right angle . Vertexo Ray 2 . We can identify

The Measure of an Angle measure an angle In geometry, we measure an angle by the smallest amount of rotation about the vertex from one side to the other

Types of Triangles And Angle Sum Theorems. Notation for sides. AB CB AC Angles ABC or B Vertex angle Base angle Opposite side Opposite

Session 4 Angle Measurement - Learner · Session 4 Angle Measurement ... You will review appropriate notation and describe angles ... the central angle has its vertex at the center

Exponential Graphs. Warm Up Solve: Find the Vertex:

Splash Screen. Concept Angle 3 and angle ABC have a common interior space a common vertex and No common interior Angle 3 and angle ABC do not have a common

Holt Algebra 2 13-1 Right-Angle Trigonometry 13-1 Right-Angle Trigonometry Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson

Angles, Triangles and Quadrangles. Vocabulary - please add these to your journals. angle vertex right angle quadrangle quadrilateral parallelogram polygon

cms5.revize.comcms5.revize.com/revize/williamsvilleschools... · b. Name the vertex of the angle. c. d. Name the sides of the angle. Name the angle in four ways. D Right Angle —

Isosceles Triangle ABC Vertex Angle Leg Base Base Angles

Vertex the point where two lines, line segments, or rays meet to form an angle Point A is a vertex for the angles formed. A

Warm Up Find the measure of the third angle in the triangle, given two angle measures

Lesson 10.2 Arcs and Chords. Arcs of Circles Central Angle-angle whose vertex is the center of the circle. central angle

Section 2.1 Angles and Their Measure. Vertex Initial Side Terminal side Counterclockwise rotation Positive Angle

· Web viewProof of Theorems 3.7, 3.8, 3.9 Let be a right triangle, the right angle being at the vertex and with the size of the angle at vertex being . Finally, we prove Theorem

CHAPTER 5 SECTION 5SECTION 5--11SECTION 5 LINES ANGLE –the union of two rays with a common endpoint. VERTEX – endpoint of an angle A C B• • • Right Angle measures exactly

Holt Geometry 5-1 Perpendicular and Angle Bisectors 5-1 Perpendicular and Angle Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation

Vertex--The Third Angle X

Warm Up Give the coordinate of the vertex of each function

November 19, 2009. A central angle of a circle is an angle with its vertex at the center of the circle. The figurebelow illustrates

Holt McDougal Geometry 12-5 Angle Relationships in Circles 12-5 Angle Relationships in Circles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson

Chapter 9 Summary - DR. EVES · • A central angle is an angle of a circle whose vertex is the center of the circle . • An inscribed angle is an angle of a circle whose vertex

Inscribed Angles. Inscribed Angles and Central Angles A Central angle has a vertex that lies in the center of a circle. A n inscribed angle has a vertex

Chapter 7: Proportions and Similarity · •Inscribed angle: an angle inside the circle with sides that are chords and a vertex on the edge of the circle •Inscribed angle = ½ intercepted

8-3 Line and Angle Relationships Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of…

Warm-up 1)What 1)What is the notation for angle with vertex at A and whose rays pass through points B and C? 2)What 2)What is the definition of an angle?

Example 1.Name all angles with B as a vertex. 2. Name the sides of angle 5. 3. Write another name for angle 6

1.4 Angles and their Measures. “angle CAB”“angle BAC” You can use the vertex of an angle to…