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Chapter 5: Q24 (page 176)

Given: PlaneX鈭�PlaneY;LM炉鈮�ON炉

Prove: LMNO is a parallelogram.

Short Answer

Expert verified

As LM and ON are parallel and congruent to each other, LMNO is a parallelogram.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

From the given diagram it can be noticed that LM and ON are the lines lying on plane X and plane Y respectively.

As plane X is parallel to plane Y and lines LM and ON are the lines lying on plane X and plane Y respectively.

Therefore, it can be said that the lines LM and ON are parallel to each other.

03

Step 3. Description of step.

It is being given that LM炉鈮�ON炉.

Therefore, it can be noticed that LM and ON are parallel and congruent to each other.

If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Therefore, as LM and ON are parallel and congruent to each other, LMNO is a parallelogram.

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