We can use proofs to show that various angles have particular values or equivalences or as we will practice in this lesson, use proofs to verify relationships within quadrilaterals.

Examples

Question 1

Prove that $x$x and $y$y are complementary angles.

Question 2

Let $s$s be the sum of exterior angles in quadrilateral $BCEG$BCEG. By using the fact that the angle sum of a quadrilateral is $360^\circ$360°, show that $s=360$s=360

Outcomes

9.G.Q.1

The diagonal divides a parallelogram into two congruent triangles. In a parallelogram opposite sides are equal and conversely. In a parallelogram opposite angles are equal and conversely. A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. In a parallelogram, the diagonals bisect each other and conversely.

9.G.Q.2

In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and (motivate) its converse.

Proofs with Quadrilaterals