In other modules, we defined a quadrilateral to be a closed plane figure bounded by four intervals, and a convex quadrilateral to be a quadrilateral in which each interior angle is less than 180°. We proved two important theorems about the angles of a quadrilateral:
The sum of the interior angles of a quadrilateral is 360°.
The sum of the exterior angles of a convex quadrilateral is 360°.
To prove the first result, we constructed in each case a diagonal that lies completely inside the quadrilateral. This divided the quadrilateral into two triangles, each of whose angle sum is 180°.
To prove the second result, we produced one side at each vertex of the convex quadrilateral. The sum of the four straight angles is 720° and the sum of the four interior angles is 360°, so the sum of the four exterior angles is 360°.
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PARALLELOGRAMS
We begin with parallelograms, because we will be using the results about parallelograms when discussing the other figures.
Step-by-step explanation:
Introductory plane geometry involving points and lines, parallel lines and transversals, angle sums of triangles and quadrilaterals, and general angle-chasing.
The four standard congruence tests and their application in problems and proofs.
Properties of isosceles and equilateral triangles and tests for them.
Experience with a logical argument in geometry being written as a sequence of steps, each justified by a reason.
Ruler-and-compasses constructions.
Informal experience with special quadrilateral
