Conjecture: PQ = ½ (AD – BC). 2.In quadrilateral ABCD, the measures of angles A, B, C and D, in that order, form an increasing arithmetic sequence.

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Presentation transcript:

Conjecture: PQ = ½ (AD – BC)

2.In quadrilateral ABCD, the measures of angles A, B, C and D, in that order, form an increasing arithmetic sequence. Explain why sides AB and CD and must be parallel. AB C D xx + d x + 2d x + 3d 4x + 6d = 360  2x + 3d = 180 2x + 3d Therefore,  B and  C are supplementary and they are same-side interior angles. Therefore, AB // DC.

3.The sum of the measures of the first three interior angles of a pentagon is 345. The measure of the fourth angle is the average of the measures of the first three. Compute the number of degrees in the measure of the fifth angle The measure of the fourth angle is = 115 . Therefore, the measure of the fifth angle is 540 – ( ) = 80 . The sum of the measures of the angles of a pentagon is 540  80 

4.The lengths of three consecutive sides of a quadrilateral are equal. If the angles included between these sides have measures of 60 degrees and 70 degrees, what is the measure of the largest angle of the quadrilateral? 