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Found in: Page 212


Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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Short Answer

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

If mA+mB180° then mD+mC180°.

Hence proved that if mA+mB180° then mD+mC180°.

See the step by step solution

Step by Step Solution

Step 1. Define contrapositive statement

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’.

The given statement is if mA+mB180° then mD+mC180°.

Step 2. Let the given statement and find its contrapositive

The contrapositive of the given statement is if mD+mC=180° then mA+mB=180°.

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:

mA+mB+mD+mC=360° mA+mB+180o=360° mA+mB=360°-180° mA+mB=180°

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