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?

Chapter 4 Angles and Measurement 4.1 Angle Measure

Protractor Postulate. For every angle Athere corresponds a positive real number less than or equal to 180. This is symbolized 0<m ∠ A ≤180. Note: m ∠A m ∠A means the measure of an angle where as ∠A ∠A is just the angle shape. Definition: The measure measure of an angle is the real number that corresponds to a particular angle. Angles are measured in degrees. A circle is broken into 360 equal divisions called degrees. The instrument used to measure angles is called a protractor.

Postulate 4.2 Continuity Postulate. If k is a half- plane determined by AC, then for every real number, 0< x ≤180, x ≤180, there is exactly one ray, AB, that lies in k such that m ∠ BAC ∠ BAC = x. Angles are classified according to their angle measure: Angle nameAngle measureAngle nameAngle measure Acute angle0°< x < 90° Angle nameAngle measure Acute angle0°< x < 90° Right anglex = 90° Angle nameAngle measure Acute angle0°< x < 90° Right anglex = 90° Obtuse angle90° < x < 180° Angle nameAngle measure Acute angle0°< x < 90° Right anglex = 90° Obtuse angle90° < x < 180° Straight angleX = 180°

Congruent angles are angles that have the same measure. Since the measures of the two angles are equal the two angles are congruent. In symbols: Since m ∠ BAC= m ∠ BAC= m ∠ YXZthen ∠ BAC ∠ BAC ≅∠ YXZ Y B C XA Z 50°

Cont of 4.1 Angle Measure Cont of 4.1 Angle Measure

Warm-up 1)Make 1)Make a table of the 4 different angles we learned about. Make sure to include the possible angle measures for each.

Cont of 4.1 Angle Measure

Geometry Tools Straight Edge Edge – is any tool that can be used to draw a straight line. Compass Compass – is a tool that has two points that come in contact with a surface. One point is a stationary point and the other marks the surface. -This tool is used to make arcs or circles. Protractor Protractor – is a tool that is used to measure angle measures. Ruler Ruler – is a tool that is used to measure segment length.

Sketch vs Draw vs Construct. When you sketch sketch a geometric figure you use just a pencil and no other tools. When you construct construct a geometric figure you use only a straight edge and a compass. When you draw draw a geometric figure you can use any tools, including tools used for measuring.

Drawing and measuring angles. To measure the degree of an angle: 1) place the hole or vertical slash mark of the protractor at the vertex of the angle. 2) Align one ray with the zero mark of the protractor. 3)The place where the other ray intersects the protractor indicates the measure of the angle.

Drawing and measuring angles. To draw an angle: 1) Draw a ray, this will be one side of the angle. 2) Place protractor so that the vertex is on the hole or vertical slash mark of the protractor. 3) Make sure the zero mark is along the original ray. 4) Mark a point at the desired angle measure. 5) Draw a ray that goes from the vertex of the original ray through the point.