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Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Warm-up
1.
4.6 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
TheoremsTheorem: 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.
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