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Chapter 4: Q.14 (page 165)

State whether the given information be used to prove that two lines are parallel and also state which lines.

m鈭�2=m鈭�6

Short Answer

Expert verified

The given condition can prove two lines parallel and the lines that are parallel are a鈭�b.

Step by step solution

01

Step 1.  Consider the diagram. 

Here, m鈭�2=m鈭�6.

02

Step 2.  Show the calculation.

Using the theorem which states-

If two lines are cut by a transversal and alternate interior angle are congruent, then lines are parallel.

Since, angle 鈭�2 and 鈭�6 are alternate interior angles, the line c is the transversal cutting the lines a and b, which are parallel to each other.

So, a鈭�b

03

Step 3.  State the conclusion.

Therefore, the condition m鈭�2=m鈭�6 proves a鈭�b.

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