Chapter 6.3, Problem 13WE

To determine

To prove: $EFGH$ is not a convex quadrilateral.

Explanation of Solution

Given information:

quad. $EFGH$ in which $m\angle EFG=93°$ ; $m\angle FGH=20°$ ; $m\angle GHE=147°$ ; $m\angle HEF=34°$

Calculation:

An indirect proof is initiated by assuming temporarily that need to prove is untrue and then work from there to finally conclude that the assumption is untrue.

Proof:

Assume temporarily that $EFGH$ is a convex quadrilateral.

From the definition of a convex quadrilateral, the sum of its interior angles should be equal to $360°$ .

When sum of angles of this quadrilateral add up, to get $294°$ which is less than $360°$ .

Therefore, the assumption that $EFGH$ is a convex quadrilateral is not true.

Hence, it is proved that $EFGH$ is not a convex quadrilateral.