Lesson 5-4 The Triangle Inequality. Ohio Content Standards:
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Transcript of Lesson 5-4 The Triangle Inequality. Ohio Content Standards:
Lesson 5-4Lesson 5-4
The Triangle The Triangle InequalityInequality
Ohio Content Ohio Content Standards:Standards:
Ohio Content Ohio Content Standards:Standards:
Describe and apply the properties of similar and congruent figures; and
justify conjectures involving similarity and congruence.
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.
Ohio Content Ohio Content Standards:Standards:
Use coordinate geometry to represent and examine the
properties of geometric figures.
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.
Theorem 5.11Theorem 5.11Triangle Inequality Triangle Inequality
TheoremTheorem
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.
Determine whether the given measures can be the lengths of
the sides of a triangle.
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
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
A.A. 77 B. 9B. 9C. 11C. 11 D. D. 1313
? becannot measureWhich
.2.5 and ,2.7 ,In
PR
QRPQPQR
Theorem 5.12Theorem 5.12
Theorem 5.12Theorem 5.12
The perpendicular segment from a point to
a line is the shortest segment from the point
to the line.
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
Corollary 5.1Corollary 5.1
Corollary 5.1Corollary 5.1
The perpendicular segment from a
point to a plane is the shortest
segment from the point to the plane.
Assignment:Assignment:
Pgs. 264-266 Pgs. 264-266 14-36 evens, 14-36 evens, 42-44 evens42-44 evens