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Chapter 4: Q.16 (page 165)

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

Given: MN炉鈮�MP炉; 鈭�NMO鈮�鈭�PMO.

Prove:MO鈫�is the 鈯�bisector of NP炉.

Short Answer

Expert verified

MO鈫� is the perpendicular bisector of NP炉.

Step by step solution

01

Step 1.  Consider the diagram. 

Here, MN炉=MP炉 and 鈭�NMO鈮�鈭�PMO.

02

Step 2.  Show the calculation.

Consider the 螖MNO and 螖MPO:

MN炉鈮�MP炉

鈭�NMO鈮�鈭�PMO

MO炉鈮�MO炉

So, by SAS Postulate, 螖MNO鈮�螖MPO.

So, NO炉鈮�PO炉.

Hence, by Theorem 4-6, MO鈫� is the perpendicular bisector of NP炉.

03

Step 3.  State the conclusion.

Therefore, MO鈫� is the perpendicular bisector of NP炉 (proved).

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Most popular questions from this chapter

For the following figure, do the SAS postulates justify that the two triangles are congruent?

Find the values of x and y.

29. In 螖JKL,JK炉鈮�KL炉,m鈭�J=2x-y,m鈭�K=2x+2yandm鈭�L=x+2y

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鈭�ACB鈮�鈭�ABC;鈭�DCB鈮�鈭�DBC

Name a pair of congruent triangles. Prove that your answer is correct.

Name the coordinates of two possible points H such that

ART


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