4th_Quarter_Lesson_4 for grade 1 and 2 only

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1. PARALLEL LINES 4th Quarter- LESSON #4

2. Objectives To Identify the congruent angles when a line transverses parallel lines. Define transversal, parallel lines and congruent angles. Demonstrate an understanding of the geometric rules that apply to transversals.

3. Parallel lines in a plane are straight lines that do not intersect at any point even when extended indefinitely in both directions. When two parallel lines are cut or intersected by another line, we call that line a transversal. The intersection points of the three lines produce angles with special relations and properties.

4. PARALLEL LINES AND TRANSVERSAL POSTULATE AND THEOREMS Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the resulting corresponding angles are congruent. Converse of Corresponding Angles Postulate: If two corresponding angles result from an intersection of two lines a and b and a transversal, then the two lines a and b are parallel. Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

5. Converse of Alternate Interior Angles Theorem: If two lines are cut by a transversal such that the alternate interior angles are congruent, then the lines are parallel.

6. Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the resulting alternate exterior angles are congruent.

7. Converse of Alternate Exterior Angles Theorem: If two lines are cut by a transversal such that the alternate exterior angles are congruent, then the lines are parallel.

8. 2. Refer to the same figure above. Given that line AB is parallel to line CD, find the value of x if m <2 = x + 51 and m <7 = 3x -99 Since there is a pair of parallel lines and a transversal, we can use the angle relationship theorems we discussed earlier. Note that <2 and <7 are alternate exterior angles. Therefore, we can use the Alternate Exterior Angles Theorem to equate the two angles.

9. x + 51 = 3x -99 x + 51 - x = 3x - 99 - x 51 = 2x - 99 51 + 99 = 2x - 99 + 99 150 = 2x 75 = x

10. ASSESSMENT A. Proving: Use a two-column table to prove the following statements. Refer to the following figure below. 1. Prove that <3 and <5 are supplementary. 2. Prove that <1 and <7 are supplementary. B. Solve: Refer to the same figure on the right. Given that m 1 = (9x + 12)°, m 6 = (3x)°and m 8 = (4y -10)° solve for x and y.

11. C. Mathematical Reasoning: Read and analyze the questions below. Explain your answers fully. 1. Is it possible for alternate interior angles formed by two parallel lines and a transversal to be congruent and supplementary at the same time?

12. D. Angle Puzzle: Solve for the missing angles using the theorems discussed above. Given that lines AH, BI, CJ, and DK are parallel to each other, solve for the missing angles <1 to <7