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Name and classify angles. Measure and construct angles and angle bisectors.

Objectives. Name and classify angles. Measure and construct angles and angle bisectors. An angle is formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices ).

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Name and classify angles. Measure and construct angles and angle bisectors.

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  1. Objectives Name and classify angles. Measure and construct angles and angle bisectors.

  2. An angleis formed by two rays, or sides, with a common endpoint called the vertex(plural: vertices).

  3. The set of all points between the sides of the angle is the interior of an angle. The exterior of an angleis the set of all points outside the angle. Angle Name R, SRT, TRS, or 1

  4. Check It Out! Example 1 Write the different ways you can name the angles in the diagram. RTQ, T, STR, 1, 2

  5. The measureof an angle is usually given in degrees. Since there are 360° in a circle, one degreeis of a circle. http://www.youtube.com/watch?v=Vio9bHLMNSM&safe=active https://www.youtube.com/watch?v=_n3KZR1DSEo&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n https://www.youtube.com/watch?v=dYHLUrFoJjc

  6. Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC  DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent.

  7. –48°–48° Example 2: Using the Angle Addition Postulate mDEG = 115°, and mDEF = 48°. Find mFEG mDEG = mDEF + mFEG  Add. Post. 115= 48+ mFEG Substitute the given values. Subtract 48 from both sides. 67= mFEG Simplify.

  8. Example 3 mXWZ = 121° and mXWY = 59°. Find mYWZ. mYWZ = mXWZ – mXWY  Add. Post. mYWZ= 121– 59 Substitute the given values. mYWZ= 62 Subtract.

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

  10. KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM. Example 4: Finding the Measure of an Angle

  11. QS bisects PQR, mPQS = (5y – 1)°, and mPQR = (8y + 12)°. Find mPQS. http://www.youtube.com/watch?v=2dhB6HHLBGM&safe=active Example 5 Find the measure of each angle.

  12. Lesson Quiz: Part I Classify each angle as acute, right, or obtuse. 1. XTS acute right 2. WTU 3. K is in the interior of LMN, mLMK =52°, and mKMN = 12°. Find mLMN. 64°

  13. Lesson Quiz: Part II 4. mWYZ = (2x – 5)° and mXYW = (3x + 10)°. Find the value of x. 35

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