*Quadrilateral I have exactly four sides and angles. If you add all of my angles together, then you would have 360 0.

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Presentation transcript:

*Quadrilateral I have exactly four sides and angles. If you add all of my angles together, then you would have 360 0

*Trapezoid I have only one set of parallel sides.

*Parallelogram I have: - 2 sets of parallel sides - 2 sets of congruent sides - opposite angles congruent - consecutive angles supplementary

*Rectangle I have all of the properties of the parallelogram PLUS - 4 right angles

*Rhombus I have all of the properties of the parallelogram PLUS - 4 congruent sides

*Square Hey, look at me! I have all of the properties of the parallelogram AND the rectangle AND the rhombus. I have it all!

Examples

3. If one angle of a parallelogram is 60 degrees, find the number of degrees in the remaining 3 angles. 12 3

3. If one angle of a parallelogram is 60 degrees, find the number of degrees in the remaining 3 angles. Since consecutive angles are supplementary, angle 1 and 60 0 must add up to Angle 2 is opposite of 60 0, therefore angle to is equal to Angle 3 is opposite of angle 1, therefore angle 1 and angle 3 are congruent. 12 3

3. If one angle of a parallelogram is 60 degrees, find the number of degrees in the remaining 3 angles. Since consecutive angles are supplementary, angle 1 and 60 0 must add up to Angle 2 is opposite of 60 0, therefore angle to is equal to Angle 3 is opposite of angle 1, therefore angle 1 and angle 3 are congruent Angle 1 = Angle 2 = 60 0 Angle 3 = 120 0

4. Find the number of degrees of each angle in the quadrilateral. 2x xx

4. Find the number of degrees of each angle in the quadrilateral. 2x xx All quadrilaterals have So, x + x + 2x + 2x = 360 6x = 360 x = 60

4. Find the number of degrees of each angle in the quadrilateral. 2x xx All quadrilaterals have So, x + x + 2x + 2x = 360 6x = 360 x = 60 Angle A = Angle B = 60 0 Angle C = 60 0 Angle D = B D C A

Practice Problems

Which statements describe the properties of a trapezoid? a. The bases are parallel. b. The diagonals are congruent. c. The opposite angles are congruent. d. The base angles are congruent.

Which statements describe the properties of a rhombus? a. The diagonals are perpendicular. b. The diagonals are congruent. c. The diagonals bisect each other. d. The diagonals bisect the angles.

If one angle of a parallelogram is 60 degrees, find the number of degrees in the remaining 3 angles.

In rhombus MATH, MA = y + 8 and AT = 4y - 7. Find MA.