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1.3 Measuring and Constructing Angles.notebook August 17, 2016 In your Foldable (Angles Section) An angle ( ) is a figure formed by two rays, or sides, with a common endpoint called the vertex. ex ter on ior B Vertex A interior 1 Names for this angle: BAC CAB A* 1 o exterino r C * The one-letter name can only be used if the angle does not share a vertex with any other angle. Congruent angles are angles that have the same measure. m∠ABC = m∠DEF ∠ABC ≅ ∠DEF Arc marks are used to show that the two angles are congruent. An angle bisector is a ray that divides an angle into two congruent angles. JK bisects ∠LJM; thus ∠LJK ≅ ∠KJM. 1 1.3 Measuring and Constructing Angles.notebook August 17, 2016 What we will learn today: ~ To name, measure, and classify angles ~ Apply the properties of congruent angles and angle bisectors An angle ( ) is a figure formed by two rays, or sides, with a common endpoint called the vertex. ex ter on ior B Vertex A 1 interior Names for this angle: BAC CAB A* 1 o exterino r C * The one-letter name can only be used if the angle does not share a vertex with any other angle. Example 1: Naming Angles A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D. Name three of the angles. B A C D 2 1.3 Measuring and Constructing Angles.notebook August 17, 2016 Measuring and Classifying Angles Measure each angle to the nearest degree. Classify the angles as acute, right, or obtuse. 1. 2. 3. 4. JHI 40o, acute IHK 90o, right JHM 90o, right MHI 130o, obtuse 3 1.3 Measuring and Constructing Angles.notebook August 17, 2016 Examples: Using the Angle Addition Postulate (a) If m<DEG = 115°, and m<DEF = 48°. Find m<FEG. (b) m<XWZ = 121° and m<XWY = 59°. Find m<YWZ. 4 1.3 Measuring and Constructing Angles.notebook August 17, 2016 Congruent angles are angles that have the same measure. m∠ABC = m∠DEF ∠ABC ≅ ∠DEF Arc marks are used to show that the two angles are congruent. An angle bisector is a ray that divides an angle into two congruent angles. JK bisects ∠LJM; thus ∠LJK ≅ ∠KJM. 5 1.3 Measuring and Constructing Angles.notebook August 17, 2016 Examples: Finding the measure of an angle (a) KM bisects <JKL, m<JKM = (4x + 6)°, and m<MKL = (7x – 12)°. Find m<JKM. (b) QS bisects <PQR, m<PQS = (5y -1)°, and m<PQR = 68°. Find m<PQS. 6