Question

WARNING I REALLY NEED HELP!!!
Developing Proof -Provide the reason for each step.
Given: I || m, <2 ≅ <4
Prove: n || p

Statements
1. I || m
2. <1 ≅ <2
3. <2 ≅ <4
4. <1 ≅ <4
5. n || p

Reasons
1. ______?
2. ______?
3. ______?
4. ______?
5. ______?

Answer 1

Example 1 Identify Parallel Lines State which lines, if any, are parallel. State the postulate or theorem that justifies your answer. p | | q since both p and q lie in the same plane, and are perpendicular to the same line, m. Example 2 Solve Problems with Parallel Lines Find x and mABC so that p ║ q. Explore From the figure, you know that mABC = 3x + 40 and mDFG = 7x - 72. You also know that ABC and DFG are alternate exterior angles. Plan For line p to be parallel to line q, the alternate exterior angles must be congruent. So, mABC = mDFG. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find mABC. Solve mABC = mDFG Alternate exterior angles 3x + 40 = 7x - 72 Substitution. 40 = 4x - 72 Subtract 3x from each side. 112 = 4x Add 72 to each side. 28 = x Divide each side by 4. Now use the value of x to find mABC. mABC = 3x + 40 Original equation = 3(28) + 40 x = 28 = 124 Simplify. Check Verify the angle measure by using the value of x to find mDFG. That is, 7x - 72 = 7(28) - 72 or 124. Since mABC = mDFG, ABC  DFG and p ║