Lesson 5-4 The Triangle Inequality. Ohio Content Standards:
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Transcript of Lesson 5-4 The Triangle Inequality. Ohio Content Standards:
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Lesson 5-4Lesson 5-4
The Triangle The Triangle InequalityInequality
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Ohio Content Ohio Content Standards:Standards:
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Ohio Content Ohio Content Standards:Standards:
Describe and apply the properties of similar and congruent figures; and
justify conjectures involving similarity and congruence.
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Ohio Content Ohio Content Standards:Standards:
Make and test conjectures about characteristics and
properties (e.g., sides, angles, symmetry) of two-dimensional figures and
three-dimensional objects.
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Ohio Content Ohio Content Standards:Standards:
Use coordinate geometry to represent and examine the
properties of geometric figures.
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Ohio Content Ohio Content Standards:Standards:
Establish the validity of conjectures about geometric objects, their properties and
relationships by counter-example, inductive and
deductive reasoning, and critiquing arguments made by
others.
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Theorem 5.11Theorem 5.11Triangle Inequality Triangle Inequality
TheoremTheorem
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Theorem 5.11Theorem 5.11Triangle Inequality Triangle Inequality
TheoremTheorem
The sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.
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Determine whether the given measures can be the lengths of
the sides of a triangle.
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Determine whether the given measures can be the lengths of
the sides of a triangle.
6 ½, 6 ½, 14 ½6 ½, 6 ½, 14 ½
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Determine whether the given measures can be the lengths of
the sides of a triangle.
6.8, 7.2, 5.16.8, 7.2, 5.1
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A.A. 77 B. 9B. 9C. 11C. 11 D. D. 1313
? becannot measureWhich
.2.5 and ,2.7 ,In
PR
QRPQPQR
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Theorem 5.12Theorem 5.12
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Theorem 5.12Theorem 5.12
The perpendicular segment from a point to
a line is the shortest segment from the point
to the line.
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Theorem 5.12Theorem 5.12
The perpendicular segment from a point to
a line is the shortest segment from the point
to the line.
A B
P
shortestdistance
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Corollary 5.1Corollary 5.1
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Corollary 5.1Corollary 5.1
The perpendicular segment from a
point to a plane is the shortest
segment from the point to the plane.
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Assignment:Assignment:
Pgs. 264-266 Pgs. 264-266 14-36 evens, 14-36 evens, 42-44 evens42-44 evens