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Chapter 6: Q21. (page 212)

Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.

If m鈭�A+m鈭�B鈮�180掳then m鈭�D+m鈭�C鈮�180掳.

Short Answer

Expert verified

Hence proved that ifm鈭�A+m鈭�B鈮�180掳 then m鈭�D+m鈭�C鈮�180掳.

Step by step solution

01

Step 1. Define contrapositive statement

If the given statement is 鈥樷�橧f p then q鈥欌��, the contrapositive is 鈥樷�橧f not q then not p鈥欌赌�.

The given statement is ifm鈭�A+m鈭�B鈮�180掳 then m鈭�D+m鈭�C鈮�180掳.

02

Step 2. Let the given statement and find its contrapositive

The contrapositive of the given statement is if m鈭�D+m鈭�C=180掳then m鈭�A+m鈭�B=180掳.

03

Step 3. Prove the statement

Since the sum of all angles of a quadrilateral is 360, therefore following will hold from the given figure as:

m鈭�A+m鈭�B+m鈭�D+m鈭�C=360掳m鈭�A+m鈭�B+180o=360掳m鈭�A+m鈭�B=360掳-180掳m鈭�A+m鈭�B=180掳

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