CHOOSE THE CORRECT ANSWER.

Pre-test Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper. 1. Which statement is not true? A. Perpendicular lines always form a right angle. B. Lines that form a right angle are parallel lines. C. Parallel lines are always the same distance apart. D. Two lines are parallel if and only if they lie in the same plane and do not intersect. 2. Refer to Figure 1, a d with e as the transversal. What must be true about 23 and 24 if b |c with e, also as the transversal? A. 23 is greater than 24. B. 23 is congruent to 24. C. 23 is a supplement of 24. Figure 1 D. 23 is a complement of 24. 3. Refer to Figure 2. Lines m and n are parallel cut by transversal t which is also perpendicular to m and n. Which statement is not correct? A. 21 and 26 are congruent. 1 2 3 4 5 6 7 B. 22 and 23 are supplementary. C. 23 and 25 are congruent angles. D. 21 and 24 form a linear pair. Figure 2D. Two lines are parallel if and only if they lie in the same plane and do not intersect. 2. Refer to Figure 1, a d with e as the transversal. What must be true about 23 and 24 if b c with e, also as the transversal? A. 23 is greater than 24. B. 23 is congruent to 24. de C. 23 is a supplement of 24. Figure 1 D. 23 is a complement of 24. 3. Refer to Figure 2. Lines m and n are parallel cut by transversal t which is also perpendicular to m and n. Which statement is not correct? 1 2 3 4 5 6 7 8 A. 21 and 26 are congruent. B. 22 and 23 are supplementary. C. 23 and 25 are congruent angles. Figure 2 D. z1 and 24 form a linear pair.a b 4. Refer to figure 3. What theorem proves, if a I c and b 1 c, then a |b? A. Two lines are parallel if they do not intersect. B. Two lines are perpendicular if they intersect at right angles. C. In a plane, if two lines are perpendicular to the same line, the the two lines are parallel. D. Given a line and a point on the line, there is only one line through Figure 3 the given point that is perpendicular to the given line. 5. Refer to Figure 4. I and 42 are cut by transversals m and n. 450 What value of x will make m 1 12? A. 6 B. 9 C. 12 D. 15 Figure 4Reflection You have accomplished the task successfully. This shows that you learned the important concepts in this module. To end this lesson meaningfully and to welcome you to the next module, I want you to accomplish this. - In this unit I learned about ... These concepts can be used in ... I understand that ...a b 4. Refer to Figure 3. What theorem proves, if a 1 c and b 1 c, then a b? A. Two lines are parallel if they do not intersect. B. Two lines are perpendicular if they intersect at right angles. C- C. In a plane, if two lines are perpendicular to the same line, the the two lines are parallel. D. Given a line and a point on the line, there is only one line through Figure 3 the given point that is perpendicular to the given line. 5. Refer to Figure 4. 4, and 4 are cut by transversals m and n. 450 2 What value of x will make m 1 lz? A. 6 B. 9 C. 12 D. 15 37 Figure 4Activity 1 Given the following information, determine which lines, if any, are parallel. State the postulates or theorems that support your answer. 1. 213 = 26 1 2 3/4 2. 48 = 216 5 6 7/8 3. 25 = 27 9/10 11/12 4. m27 + mz11 = 180 13/14 15/16 5. m23 + m28 = 180 p Activity 2 A. Find the value of x so that s II c. 1. 2. (11x - 5) R C (12x - 4)" 16 148 CB. Find the value of x so that j Ir. 1. 2. (5x - 10)" (x +70) (6x + 10) Activity 3 Fill the missing statements and reasons. Given: p 1 j n l j 1 2 Prove: pll n V MATH 8 QUARTER 4 WEEK 5 Page 7 | 11Proof: Statements Reasons 1. Given 21 is a right angle. 2. 3. Definition of Perpendicular Lines 41 = 42 4. pln 5.6% \".54.. Remember 'I'wo lines are parallel if and only if they lie in the same plane and do not intersect. Parallel lines never cross. To prove that the two lines or segments are parallel, you must show that one of the following is true. Converse of Corresponding Angles Posh-[late If two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the lines are parallel. Converse ofternnbe Interior Angles Theorem If two lines are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel. Converse ofternnbe Exterior Angles Theorem If two lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are parallel. Converse of Esme-Bide Interior Angles Theorem If two lines are cut by a transversal so that a pair of sameside interior angles is supplementary, then the lines are parallel. Converse of Esme-Bide Exterior Angles Theorem If two lines are cut by a transversal so that a pair of sameside exterior angles is supplementary, then the lines are parallel. Two lines are perpendicular if and only if they form a right angle. To prove that two lines are perpendicular, you must show that one of the following is true: 1. If two lines are perpendicular, then they form four right angles. 2. If the angles in a linear pair are congruent, then the lines containing their sides are perpendicular. 3. If two angles are adjacent and complementary, the non-common sides are perpendicular. Check your Understanding A. Lines p and q are cut by a transversal, find the value of x that makes p Il q. 1. 24 and 25 are alternate interior angles, mz4 = 5x - 11 and m 25 = 3x +7. 2. 24 and 26 are same side interior angles, mz4 = 6x + 3 and m 26 = 4x + 7. 3. 22 and 26 are corresponding angles, mz2 = 3x -15 and m 26 = x + 55.B. Find the value of x so that min. 1. 2. 7 m Am (6x + 6) (3x + 5) (8x - 22) 40 n C. Write a two-column proof for each. 1. Given: I ll o 6 48 = 27 9 Prove: a ll d V d Proof:Statements Reasons Post Test Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper. 1. Which statement is not true? A. Perpendicular lines always form a right angle. B. Lines that form a right angle are parallel lines. C. Parallel lines are always the same distance apart. D. Two lines are parallel if and only if they lie in the same plane and do not