Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Warm-up 1. 4.6 Conditions for Special Quadrilaterals.

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Presentation transcript:

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Warm-up Conditions for Special Quadrilaterals

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 4.6 Conditions for Special Quadrilaterals Theorems Theorem: If two pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem: If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. Theorem: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 4.6 Conditions for Special Quadrilaterals Theorems Theorem: If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle. The Housebuilder Theorem: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Theorem: If one pair of adjacent sides of a parallelogram are congruent, then the parallelogram is a rhombus.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 4.6 Conditions for Special Quadrilaterals Theorems Theorem: If the diagonals of a parallelogram bisect the angles of the parallelogram, then the parallelogram is a rhombus. Theorem: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. The Triangle Midsegment Theorem: A midsegment of a triangle is parallel to a side of the triangle and has a measure equal to half the measure of that side.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 4.6 Conditions for Special Quadrilaterals Classify quadrilaterals from given information. Is quadrilateral ABCD a parallelogram? Because the diagonals of ABCD bisect each other, ABCD is a parallelogram.