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Chapter 4: Q.15 (page 165)

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

鈭�8and 鈭�5 are rt. 鈭�s

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, 鈭�8 and 鈭�5 are rt. 鈭�s that is 鈭�8 and 鈭�5 are right angles.

02

Step 2.  Show the calculation.

m鈭�5+m鈭�6=180掳 鈥︹�� [linear angles]

That implies,

m鈭�6+90掳=180掳

Subtracting 90掳from each side,

m鈭�6=180掳鈭�90掳m鈭�6=90掳

So, 鈭�8鈮�鈭�6and they are corresponding angles, where cis transversal.

So, by Converse of corresponding Angles Theorem, which states that if any pair of corresponding angles is congruent, then the two lines are parallel.

So, a鈭�b.

03

Step 3.  State the conclusion.

Therefore, the condition 鈭�8 and 鈭�5 are rt. 鈭�s proves a鈭�b.

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Most popular questions from this chapter

For the following figure, can the triangle be proved congruent? If so, what postulate can be used?

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