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Download 1.4 Measure and Classify Angles
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1.4 Measure and Classify Angles You will name, measure and classify angles. Classifying Angles • Acute angle: between 0 and 90 • Right angle: exactly 90 degrees • Symbol: • Obtuse Angle: between 90 and 180 • Straight angle: exactly 180 degrees Angles • Naming Angles – Use 3 capital letters – Vertex in the middle – Can use one capital letter if it is the vertex and it is obvious which angle you are referring to – Can use the number located inside the angle • Angle Bisector – Divides the angle into 2 congruent parts Naming angles • Name this angle three different ways Naming angles • Name this angle three different ways Naming angles • Name this angle four different ways Name this angle in 4 ways Congruent Angles • Have the same angle measure Congruent Angles • Can be marked using the same number of hash marks. H W F Q Angle Addition Postulate • Smaller angles can be added together to form larger angles if they share a common vertex. Given that the m<LKN=145⁰, find the m<LKM and m<MKN GUIDED PRACTICE for Example 3 Find the indicated angle measures. 3. Given that <KLM is a straight angle, find x and m< NLM. GUIDED PRACTICE 4. for Example 3 Given that < EFG is a right angle, find x and m< HFG. Homework • Page 28 # 4 – 40 even • Honors: also # 42, 44, 48, 49, 50 EXAMPLE 2 Measure and classify angles Use the diagram to find the measure of the indicated angle. Then classify the angle. a. KHJ b. GHK c. GHJ d. SOLUTION A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use. GHL Angle Addition Postulate • When two angles share a ray, a Part+ Part = Whole or Little + Little = Big • Very similar to segment addition Postulate Congruent Angles • Angles that have the same measure • Angle measures are equal: m<A=m<B – The measure of angle A is equal to the measure of angle B • Angle measures are congruent: <A <B – Angle A is congruent to angle B • When talking about measures, use equal sign. When talking about congruency, use congruent sign EXAMPLE 4 Identify congruent angles The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m<DEG = 157° ,what is m<GKL? GUIDED PRACTICE for Example 4 Use the diagram shown. 5. Identify all pairs of congruent angles in the diagram. GUIDED PRACTICE for Example 4 Use the diagram shown. 6. In the diagram, m < PQR = 130 , m<QRS = 84, and m<TSR = 121 . Find the other angle measures in the diagram. Angle • Formed by two rays that meet at an endpoint • Rays are considered sides of an angle • What is the vertex? What rays form the angle? Vertex of an Angle • Where the sides of an angle meet. • When naming an angle, vertex goes in the middle Name the three angles in the diagram. Angle bisector A ray that divides an angle into two angles that are congruent (equal) In the diagram at the right, YW bisects < XYZ, and m< XYW = 18. Find m< XYZ. Protractor Postulate • The rays of an angle can be matched one to one with real numbers from 0 to 180 • The measure of an angle is equal to the absolute value of the difference between the real number of the rays (much like the segment addition postulate)