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Homework Review

Explore geometric theorems and properties involving lines, angles, triangles, and parallelograms. Learn to prove congruent angles in parallel lines cut by a transversal.

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Homework Review

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  1. Homework Review

  2. CCGPS Analytic GeometryDay 3 (1/13/14) UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms? Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13 Today’s Question: Which angles are congruent to each other when parallel lines are cut by a transversal? Standard: MCC9-12.A.CO.9

  3. Parallel Lines and Transversals

  4. Parallel Lines – Two lines are parallel if and only if they are in the same plane and do not intersect. B A D C AB CD

  5. Parallel Planes – Planes that do not intersect.

  6. Skew Lines – two lines that are NOT in the same plane and do NOT intersect

  7. AB, FG, DG, BC Ex 1: Name all the parts of the prism shown below. Assume segments that look parallel are parallel. 1. A plane parallel to plane AFE. F E Plane BGD G D 2. All segments that intersect GB. A C B GD, BC 3. All segments parallel to FE. 4. All segments skew to ED. BG, FA, BC

  8. Transversal – A line, line segment, or ray that intersects two or more lines at different points. a b Line t is a transversal. t

  9. Special Angles 2 1 4 Interior Angles – lie between the two lines (3, 4, 5, and 6) 3 6 5 8 7 Alternate Interior Angles– are on opposite sides of the transversal. (3 & 6 AND 4 and 5) Consecutive Interior Angles – are on the same side of the transversal. (3 & 5 AND 4 & 6)

  10. More Special Angles Exterior Angles – lie outside the two lines (1, 2, 7, and 8) 2 1 4 3 6 5 8 7 Alternate Exterior Angles – are on opposite sides of the transversal (1& 8 AND 2 & 7)

  11. Ex. 2: Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical. a. 1 and 2 1 Alt. Ext. Angles 6 7 3 b. 6 and 7 4 8 5 Vertical Angles 2 c. 3 and 4 Alt. Int. Angles d. 3 and 8 Consec. Int. Angles

  12. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent. 8 1 7 2  6 2 6 3 5 4 3  7

  13. Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are congruent. 8 1 7 1  5 2 6 3 5 4 4  8

  14. Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary. m2 + m3 = 180° 8 1 7 2 6 m6 + m7 = 180° 3 5 4

  15. Ex. 3 In the figure, pq. If m5 = 28°, find the measure of each angle. 28° q a. m8 = 2 1 p b. m1 = 28° 4 3 c. m2 = 152° 6 5 8 7 d. m3 = 152° e. m4 = 28°

  16. Ex. 4 In the figure, st. Find the mCBG. t A Step 1: Solve for x. G S B D 3x – 5 = 4x - 29 3x -5 C -5 = x - 29 4x -29 E 24 = x F Step 2: mCBG = mABE = 3x -5. 3x-5 = 3(24) – 5 = 72-5 = 67°

  17. Ex: 5Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 10 11 9 12 16 alternate exterior 8 1 15 13 7 2 6 14 3 5 4

  18. Ex: 6Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 10 11 9 12 16 consecutive interior 8 1 15 13 7 2 6 14 3 5 4

  19. Ex: 7Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 10 11 9 12 16 alternate interior 8 1 15 13 7 2 6 14 3 5 4

  20. Ex: 8Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 10 11 9 12 16 alternate exterior 8 1 15 13 7 2 6 14 3 5 4

  21. Ex: 9Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 10 11 9 12 16 consecutive interior 8 1 15 13 7 2 6 14 3 5 4

  22. Ex: 10Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 10 11 9 12 16 vertical 8 1 15 13 7 2 6 14 3 5 4

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