Exploring Special Quadrilaterals
Lesson 14
Topics
x Properties of parallelograms.
x 7KHFODVVL¿FDWLRQRISDUDOOHORJUDPVUHFWDQJOHVVTXDUHVDQGUKRPEXVHVYLDWKHLUGLDJRQDOV
Results
x In a parallelogram,
ż RSSRVLWHVLGHVRIWKH¿JXUHDUHFRQJUXHQW
ż RSSRVLWHDQJOHVRIWKH¿JXUHDUHFRQJUXHQW
ż WKHGLDJRQDOVRIWKH¿JXUHELVHFWRQHDQRWKHU
$QGWKHFRQYHUVHRIHDFKRIWKHVHKROGVWUXHͼ)RUH[DPSOHLIDTXDGULODWHUDOKDVRSSRVLWHVLGHVWKDW
DUHFRQJUXHQWWKHQWKDW¿JXUHLVDSDUDOOHORJUDPͽ
x The diagonals of a rectangle bisect one another and are congruent. Conversely, if a quadrilateral has
GLDJRQDOVWKDWELVHFWRQHDQRWKHUDQGDUHFRQJUXHQWWKHQWKDW¿JXUHLVDUHFWDQJOH
x The diagonals of a rhombus bisect one another and are perpendicular. Conversely, if a quadrilateral has
GLDJRQDOVWKDWELVHFWRQHDQRWKHUDQGDUHSHUSHQGLFXODUWKHQWKDW¿JXUHLVDUKRPEXV
x The diagonals of a square bisect one another, are congruent, and are perpendicular. Conversely, if a
quadrilateral has diagonals that bisect one another, are congruent, and are perpendicular, then that
¿JXUHLVDVTXDUH
Summary
)RXUVLGHG¿JXUHVZLWKGLDJRQDOVKDYLQJVSHFLDOSURSHUWLHVPDNHSUDFWLFDODSSHDUDQFHVLQWKHUHDOZRUOG,QWKLV
lesson, we explore the implications of imposing conditions on the diagonals of a quadrilateral.