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m  1 + m 2 = m PQR.

P. 1. Q. A. 2. R. The Angle Addition Postulate. m  1 + m 2 = m PQR. There are two equations that can be derived using Postulate 4. m  1 = m PQR – m  2. These equations are true no matter where A is located in the interior of PQR. m 2 = m PQR – m  1. C. D.

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m  1 + m 2 = m PQR.

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  1. P 1 Q A 2 R The Angle Addition Postulate m1 + m2 = mPQR. There are two equations that can be derived using Postulate 4. m1 = mPQR –m2 These equations are true no matter where A is locatedin the interior of PQR. m2 = mPQR –m1

  2. C D (5x – 6)° 2x° B A The Angle Addition Postulate Find mABC and mCBD if mABD = 120. mABC + mCBD = mABD Postulate 4 Substitution 2x + (5x – 6) = 120 7x – 6 = 120 Combine like terms 7x = 126 Add 6 to both sides x = 18 Divide each side by 7 36 + 84 = 120 mCBD = 5x – 6 mABC = 2x mCBD = 5(18) – 6 mABC = 2(18) mCBD = 90 – 6 mABC = 36 mCBD = 84

  3. Q P A B C Postulates postulates Geometry is built on statements called _________. Postulates are statements in geometry that are accepted to be true. Postulate 5: A line contains at least 2 points A plane contains at least 3 points not all in one line Space contains at least 4 points not all in one line

  4. C B Q P A l T m Postulates Postulate 6: Two points determine a unique ___. line There is only one line that containsPoints P and Q Theorem 1-1: If two distinct lines intersect, then their intersection is a ____. point Lines l and m intersect at point T Postulate 7: Three noncollinear points determine a unique _____. plane There is only one plane that contains points A, B, and C.

  5. 2) Name the intersection of Postulates Points A, B, and C are noncollinear. A 1) Name all of the different lines that can be drawn through these points. C B Point C

  6. A B D C Postulates 1) Name all of the planes that are represented in the figure.

  7. A B D C Postulates 1) Name all of the planes that are represented in the figure. There is only one plane that contains threenoncollinear points. plane ABC (side) plane ACD (side) plane ABD (back side) plane BCD (bottom)

  8. A B Postulates Postulate 8: If two points are in a plane, then the line That contains the points is in that plane The line that contains points A and B is in the plane shown.

  9. D M E N Postulates Postulate 9: If two distinct planes intersect, then their intersection is a ___. line Plane M and plane N intersect in line DE.

  10. F E A D H G B C Postulates Name the intersection of plane CDG and plane BCD.

  11. Name two planes that intersect in . F E A D H G B C Postulates Name the intersection of plane CDG and plane BCD. planes ADF and CDF

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