Quadrilateral I have exactly four sides and angles

*Quadrilateral I have exactly four sides and angles. If you add all of my angles together, then you would have 3600

*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. 1 2 3

3. If one angle of a parallelogram is 60 degrees, find the number of degrees in the remaining 3 angles. 1 2 3 Since consecutive angles are supplementary, angle 1 and 600 must add up to 1800. Angle 2 is opposite of 600, therefore angle to is equal to 600. Angle 3 is opposite of angle 1, therefore angle 1 and angle 3 are congruent.

3. If one angle of a parallelogram is 60 degrees, find the number of degrees in the remaining 3 angles. 1 2 3 Since consecutive angles are supplementary, angle 1 and 600 must add up to 1800. Angle 2 is opposite of 600, therefore angle to is equal to 600. Angle 3 is opposite of angle 1, therefore angle 1 and angle 3 are congruent. Angle 1 = 1200 Angle 2 = 600 Angle 3 = 1200

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

4. Find the number of degrees of each angle in the quadrilateral. x 2 x All quadrilaterals have 3600. So, x + 2 x = 360 6 x = 360 x = 60

4. Find the number of degrees of each angle in the quadrilateral. B C x A 2 x All quadrilaterals have 3600. So, x + 2 x = 360 6 x = 360 x = 60 x 2 x D Angle A = 1200 Angle B = 600 Angle C = 600 Angle D = 1200

Practice Problems

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

Which statements describe the properties of a rhombus? a. b. c. d. The diagonals are perpendicular. The diagonals are congruent. The diagonals bisect each other. 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 = 4 y - 7. Find MA.