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Chapter 4: Q.17 (page 165)

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

Given: MO炉鈯�NP炉; NO炉鈮�PO炉.

Prove: MN炉鈮�MP炉.

Short Answer

Expert verified

It is proved NM炉鈮�MP炉.

Step by step solution

01

Step 1.  Consider the diagram. 

Here, MO炉鈯�NP炉 and NO鈮�PO.

02

Step 2.  Show the calculation.

Consider the right angled 螖NQO and 螖PQO:

NO炉鈮�PO炉, which are hypotenuse.

QO炉鈮�QO炉, which are legs.

So, by HL Postulate, 螖NQO鈮�螖PQO.

So, NQ炉鈮�PQ炉.

Consider 螖NQM and 螖PQM:

NQ炉鈮�PQ炉

鈭�NQM鈮�鈭�PQM=90掳

QM炉鈮�QM炉

So, by SAS Postulate, 螖NQM鈮�螖PQM.

So, NM炉鈮�MP炉

03

Step 3.  State the conclusion.

Therefore, NM炉鈮�MP炉 (proved).

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

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Find the values of x and y.

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Suppose you know that DB炉鈯�DC炉.Explain how you can deduce that DB炉鈯�BA炉.
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