David Vundi Mathematics Teacher Measure and Classify Angles GEOMETRY.

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Presentation transcript:

David Vundi Mathematics Teacher Measure and Classify Angles GEOMETRY

David Vundi Objective Use angle postulates and classify angles as acute, right, obtuse, or straight

David Vundi An Angle An angle consists of two different rays (sides) with the common endpoint (vertex). D A B C 1 Interior Exterior Angle Name A, BAC, CAB, or 1

David Vundi Protractor postulate A protractor is used to approximate the measure of an angle in degrees. The rays of an angle can be matched one to one with the real numbers from 0 to 180. The measure of the angle is equal to the absolute value of the difference between the real numbers for the rays.

David Vundi

David Vundi Who uses this?

David Vundi Measure and classify angles A B C D E F Quiz

David Vundi Angle Addition Postulate

David Vundi Find Angle measures o ALGEBRA Given that m LKN =145, find m LKM and m MKN. SOLUTION STEP 1 Write and solve an equation to find the value of x. m LKN = m LKM + m MKN Angle Addition Postulate Substitute angle measures. 145 = 6x + 7 Combine like terms. Subtract 7 from each side. 138 = 6x Divide each side by 6.23 = x 145 = (2x + 10) + (4x – 3) o o o

David Vundi Find Angle measures EXAMPLE 1 STEP 2 Evaluate the given expressions when x = 23. m LKM = (2x + 10)° = ( )° = 56° m MKN = (4x – 3)° = (4 23 – 3)° = 89° So, m LKM = 56° and m MKN = 89°. ANSWER

David Vundi

David Vundi GUIDED PRACTICE Find the indicated angle measures. 3. Given that KLM is a straight angle, find m KLN and m NLM. ANSWER 125°, 55°

David Vundi GUIDED PRACTICE Given that EFG is a right angle, find m EFH and m HFG. ANSWER 60°, 30°

David Vundi Congruent Angles

David Vundi Activity

David Vundi An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK  KJM.

David Vundi

David Vundi What have we learnt? An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle. Angles that have the same measure are called congruent angles. A point is in the interior of an angle if it is between points that lie on each side of the angle. A point is in the exterior of an angle if it is not on the angle or in its interior. An acute angle has measure greater than 0 and less than 90 o. A right angle has measure equal to 90 o. An obtuse angle has measure greater than 90 o and less than 180 o. A straight angle has measure equal to 180 o. Two angles are adjacent angles if they share a common vertex and side, but have no common interior points.

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