Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the...

18
Angles

Transcript of Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the...

Page 1: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Angles

Page 2: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Angle and PointsAn Angle is a figure formed by two rays with a

common endpoint, called the vertex.

vertex

ray

rayAngles can have points in the interior, in the exterior or on the angle.

E is in the exterior.

A

BC

DE

Points A, B and C are on the angle.

D is in the interior

B is the vertex.

Page 3: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Naming an Angle

ABC or CBA Using 3 points: Vertex must be the middle letter

This angle can be named as

Using 1 point: Using only vertex letter

A

BC

B

Using a number: 2

2

Use the notation m2, meaning the measure of 2.

Page 4: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Example

K

32

K

L

M

P

Therefore, there is NO in this diagram.

Name all the angles in the diagram below

, ,LKM PKM and LKP

2 3 5!!!There is also and b Nut t Ohere is

K is the vertex of more than one angle.

Page 5: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Example

Name the three angles in the diagram.

Page 6: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

4 Types of Angles

Acute Angle: an angle whose measure is less than 90.

Right Angle: an angle whose measure is exactly 90 .

Obtuse Angle: an angle whose measure is between 90 and 180.

Straight Angle: an angle that is exactly 180 .

Page 7: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Angle Addition PostulateSame idea as the segment addition postulate

R

M K

W

The sum of the two smaller angles will always equal the measure of the larger angle.

Complete:

m ____ + m ____ = m _____MRK KRW MRW

Postulate:

Page 8: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Example

Fill in the blanks. m < ______ + m < ______ = m <

_______

Page 9: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Adding Angles

If you add m1 + m2, what is your result?

22°

36°

21

D

B

C

A

Therefore, mADC = 58.

m1 + m2 = mADC

m1 + m2 = 58.

Also…

Page 10: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Example

R

M K

W

3x + x + 6 = 90 4x + 6 = 90 – 6 = –64x = 84x = 21

K is interior to MRW, m MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK.

3xx+6

Are we done?

mMRK = 3x = 3•21 = 63º

First, draw it!

Page 11: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

ExampleGiven that m< LKN = 145, find m < LKM and m < MKN

Page 12: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

ExampleGiven that < KLM is a straight angle, find m < KLN and m < NLM

Page 13: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Example

Given m < EFG is a right angle, find m < EFH and m < HFG

Page 14: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Angle Bisector

An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles.

5

3

Page 15: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

3 5.

Congruent Angles

5

3

Definition: If two angles have the same measure, then they are congruent.

Congruent angles are marked with the same number of “arcs”.

Page 16: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

j41°

41°

64

U

K

is an angle bisectorUK

Example:

J

T

Which two angles are congruent?

<JUK and < KUT or < 4 and < 6

Page 17: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Example:Given bisects < XYZ and m < XYW = . Find m < XYZYW

??????????????18

Page 18: Angles. Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior,

Example:Given bisects < ABC. Find m < ABC

BD??????????????


What is coveredirina/1312_Review_Test2_TT_notes.pdf · 3.3 Isosceles Triangles You need to know: Terms: Isosceles Triangle, Vertex, Legs, Base, Base Angles, Vertex Angle, Angle Bisector,

What is coveredirina/1312_Review_Test2_TT_notes.pdf · 3.3 Isosceles Triangles You need to know: Terms: Isosceles Triangle, Vertex, Legs, Base, Base Angles, Vertex Angle, Angle Bisector,

Angles Related to a Circle Lesson 10.5. Angles with Vertices on a Circle Inscribed Angle: an angle whose vertex is on a circle and whose sides are determined.

Angles Related to a Circle Lesson 10.5. Angles with Vertices on a Circle Inscribed Angle: an angle whose vertex is on a circle and whose sides are determined.

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.

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.

Inscribed AnglesInscribed Angles - TypePad · Holt McDougal Geometry Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of

Inscribed AnglesInscribed Angles - TypePad · Holt McDougal Geometry Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of

hhsgeometry.files.wordpress.com · CENTRAL ANGLES VERTEX MUST BE ON THE CENTER OF THE CIRCLE. RULE: ANGLE INTERCEPTED ARC ANGLES FORMED BY 2 CHORDS "BOW -TIE ANGLES" VERTEX is NOT

hhsgeometry.files.wordpress.com · CENTRAL ANGLES VERTEX MUST BE ON THE CENTER OF THE CIRCLE. RULE: ANGLE INTERCEPTED ARC ANGLES FORMED BY 2 CHORDS "BOW -TIE ANGLES" VERTEX is NOT

Angle Relationships Day 1. Angles angle sides vertexAn angle consists of two different rays (sides) that share a common endpoint (vertex). Sides Vertex.

Angle Relationships Day 1. Angles angle sides vertexAn angle consists of two different rays (sides) that share a common endpoint (vertex). Sides Vertex.

1.4 ANGLES. The two rays are called the sides of the angle. The common endpoint of the two rays is called the vertex of the angle An angle is a geometric.

1.4 ANGLES. The two rays are called the sides of the angle. The common endpoint of the two rays is called the vertex of the angle An angle is a geometric.

Inscribed Angles 10-4. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle.

Inscribed Angles 10-4. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle.

Angles in Degree & Radian Measure w/Unit Circle. Angle Measure Standard Position: an angle in the coordinate plane with vertex at the origin and one ray(side)

Angles in Degree & Radian Measure w/Unit Circle. Angle Measure Standard Position: an angle in the coordinate plane with vertex at the origin and one ray(side)

MATH · 2017-03-16 · for the angles because none of the angles are labeled numerically. You also can’t name the angle by the vertex because point E is the vertex for all of the

MATH · 2017-03-16 · for the angles because none of the angles are labeled numerically. You also can’t name the angle by the vertex because point E is the vertex for all of the

An angle is formed when two rays meet at a point called the vertex. Angles are usually measured in degrees using a protractor. Angle measures range from.

An angle is formed when two rays meet at a point called the vertex. Angles are usually measured in degrees using a protractor. Angle measures range from.

61 Angles and PreCalc/Trig A Radian Measure...Pre Calc/Trig A 6 1 Angles and Radian Measure March 23, 2015 Central Angle: an angle whose vertex lies at the center of the circle Circular

61 Angles and PreCalc/Trig A Radian Measure...Pre Calc/Trig A 6 1 Angles and Radian Measure March 23, 2015 Central Angle: an angle whose vertex lies at the center of the circle Circular

Angles BROUGHT TO YOU BY POWERPOINTPROS.COM. What are angles? An angle is formed by 2 lines or rays diverging from a common point (known as the vertex.)

Angles BROUGHT TO YOU BY POWERPOINTPROS.COM. What are angles? An angle is formed by 2 lines or rays diverging from a common point (known as the vertex.)

12.2 – Angles and Angle Measure. Standard Position – when the vertex of the angle is at the origin and one ray is on the positive x-axis. Initial Side.

12.2 – Angles and Angle Measure. Standard Position – when the vertex of the angle is at the origin and one ray is on the positive x-axis. Initial Side.

Isosceles Triangle ABC Vertex Angle Leg Base Base Angles.

Isosceles Triangle ABC Vertex Angle Leg Base Base Angles.

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

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

1.5 Angle Relationships. Adjacent Angles Two angles that lie in the same plane, have a common vertex and a common side, but no common interior points.

1.5 Angle Relationships. Adjacent Angles Two angles that lie in the same plane, have a common vertex and a common side, but no common interior points.

Introduction All circles are similar; thus, so are the arcs intercepting congruent angles in circles. A central angle is an angle with its vertex at the.

Introduction All circles are similar; thus, so are the arcs intercepting congruent angles in circles. A central angle is an angle with its vertex at the.

1. 4.2 – Circles & Volume Inscribed Angles Name … · 1. Sec 4.2 – Circles & Volume Inscribed Angles Name: Central Angle: An angle whose vertex is the center of the circle. Inscribed

1. 4.2 – Circles & Volume Inscribed Angles Name … · 1. Sec 4.2 – Circles & Volume Inscribed Angles Name: Central Angle: An angle whose vertex is the center of the circle. Inscribed

Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted.

Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted.