Geo: Sec 5.1 Perpendiculars

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Geo Sec 5.1 Perpendiculars Bisectors
Thm 5.1 Perpendicular Bisector Theorem If a
point is on the perpendicular bisector of a
segment, then it is equidistant from the
endpoints of the segment.
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Geo Sec 5.1 Perpendiculars Bisectors
Thm 5.1 Perpendicular Bisector Theorem If a
point is on the perpendicular bisector of a
segment, then it is equidistant from the
endpoints of the segment. equidistant its
distance from each endpoint is the
same perpendicular bisector ray, segment,
line, or plane that is perpendicular to the
segment at its midpoint
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Geo Sec 5.1 Perpendiculars Bisectors
Thm 5.1 Perpendicular Bisector Theorem If a
point is on the perpendicular bisector of a
segment, then it is equidistant from the
endpoints of the segment. If CP is the
perpendicular bisector of AB, then CA CB.
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Sec 5.1 Perpendiculars Bisectors
Thm 5.2 Converse of Perpendicular Bisector
Theorem If a point is equidistant from the
endpoints of the segment, then it is on the
perpendicular bisector of the segment.
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Sec 5.1 Perpendiculars Bisectors
Thm 5.2 Converse of Perpendicular Bisector
Theorem If a point is equidistant from the
endpoints of the segment, then it is on the
perpendicular bisector of the segment. If
DA DB, then D lies on the perpendicular
bisector of AB.
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Sec 5.1 Perpendiculars Bisectors
In the diagram shown, MN is the perpendicular
bisector of ST. What segments lengths in
the diagram are equal?
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Sec 5.1 Perpendiculars Bisectors
In the diagram shown, MN is the perpendicular
bisector of ST. What segments lengths in
the diagram are equal? Solution MN bisects
ST, so NS NT. Because M is on the perpendicular
bisector of ST, MS MT. (Thm 5.1)
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Sec 5.1 Perpendiculars Bisectors
In the diagram shown, MN is the perpendicular
bisector of ST. Explain why Q is on MN.
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Sec 5.1 Perpendiculars Bisectors
In the diagram shown, MN is the perpendicular
bisector of ST. Explain why Q is on
MN. Solution QT QS so Q is equidistant
from S and T. By Thm 5.2, Q is on the
perpendicular bisector of ST, which is MN.
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Sec 5.1 Perpendiculars Bisectors
Thm 5.3 Angle Bisector Theorem If a point is
on the bisector of an angle, then it is
equidistant from the sides of the angle.
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Sec 5.1 Perpendiculars Bisectors
Thm 5.3 Angle Bisector Theorem If a point is
on the bisector of an angle, then it is
equidistant from the sides of the angle.
If m lt BAD m lt CAD, then DB DC.
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Sec 5.1 Perpendiculars Bisectors
Thm 5.4 Converse of Angle Bisector Theorem If a
point is in the interior of an angle and is
equidistant from the sides of the angle, then it
lies on the bisector of the angle.
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Sec 5.1 Perpendiculars Bisectors
Thm 5.4 Converse of Angle Bisector Theorem If a
point is in the interior of an angle and is
equidistant from the sides of the angle, then it
lies on the bisector of the angle.
If DB DC, then m lt BAD m lt CAD,
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Sec 5.1 Perpendiculars Bisectors
Roof Trusses Some roofs are built with wooden
trusses that are assembled in the factory and
shipped to the building site. In the diagram of
the roof truss shown below, you are given that AB
bisects ltCAD and that lt ACB and ltADB are right
angles.
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Sec 5.1 Perpendiculars Bisectors
Roof Trusses Some roofs are built with wooden
trusses that are assembled in the factory and
shipped to the building site. In the diagram of
the roof truss shown below, you are given that AB
bisects ltCAD and that lt ACB and ltADB are right
angles. What can you say about BC and BD ?
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Sec 5.1 Perpendiculars Bisectors
Roof Trusses Some roofs are built with wooden
trusses that are assembled in the factory and
shipped to the building site. In the diagram of
the roof truss shown below, you are given that AB
bisects ltCAD and that lt ACB and ltADB are right
angles. What can you say about BC and BD
? Solution Because BC and BD meet AC and AD _at_
right angles, they are perpendicular segments to
the sides of ltCAD. This implies that their
lengths represent the distances from pt. B to AC
and AD.
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Sec 5.1 Perpendiculars Bisectors
Roof Trusses Some roofs are built with wooden
trusses that are assembled in the factory and
shipped to the building site. In the diagram of
the roof truss shown below, you are given that AB
bisects ltCAD and that lt ACB and ltADB are right
angles. What can you say about BC and BD
? Solution Because BC and BD meet AC and AD _at_
right angles, they are perpendicular segments to
the sides of ltCAD. This implies that their
lengths represent the distances from pt. B to AC
and AD. Because pt B is on the bisector of ltCAD,
it is equidistant from the sides of the angle.
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Sec 5.1 Perpendiculars Bisectors
Roof Trusses Some roofs are built with wooden
trusses that are assembled in the factory and
shipped to the building site. In the diagram of
the roof truss shown below, you are given that AB
bisects ltCAD and that lt ACB and ltADB are right
angles. Solution Because BC and BD meet AC and
AD _at_ right angles, they are perpendicular
segments to the sides of ltCAD. This implies that
their lengths represent the distances from pt. B
to AC and AD. Because pt B is on the bisector of
ltCAD, it is equidistant from the sides of the
angle. So BC BD and BC BD.