Transcript Section 5.3

The definition of inequality and the properties of inequalities can be applied to the
measures of angles and segments, since these are real numbers. Consider 1, 2,
and 3 in the figure shown.
By the Exterior Angle Theorem, you know
that m1 = m2 + m3.
Since the angle measures are positive numbers,
we can also say that
m1 > m2
and
by the definition of inequality.
m1 > m3
Use the Exterior Angle Inequality Theorem
Use the Exterior Angle Inequality Theorem
The longest side and largest angle of ∆ABC are opposite each other. Likewise, the
shortest side and smallest angle are opposite each other.
Order Triangle Angle Measures
List the angles of ΔABC in order from smallest to
largest.
Order Triangle Side Lengths
List the sides of ΔABC in order from
shortest to longest.
Angle-Side Relationships
HAIR ACCESSORIES Ebony is following directions
for folding a handkerchief to make a bandana for
her hair. After she folds the handkerchief in half, the
directions tell her to tie the two smaller angles of
the triangle under her hair. If she folds the
handkerchief with the dimensions shown, which
two ends should she tie?
Five-Minute Check (over Lesson 5–2)
CCSS
Then/Now
Key Concept: Definition of Inequality
Key Concept: Properties of Inequality for Real Numbers
Theorem 5.8: Exterior Angle Inequality
Example 1: Use the Exterior Angle Inequality Theorem
Theorems: Angle-Side Relationships in Triangles
Example 2: Order Triangle Angle Measures
Example 3: Order Triangle Side Lengths
Example 4: Real-World Example: Angle-Side Relationships
Over Lesson 5–2
Find the coordinates of the centroid of the triangle
with vertices D(–2, 9), E(3, 6), and F(–7, 0).
A. (–4, 5)
B. (–3, 4)
C. (–2, 5)
D. (–1, 4)
Over Lesson 5–2
Find the coordinates of the orthocenter of the
triangle with vertices F(–1, 5), G(4, 4), and H(1, 1).
A.
B.
C. (2, 3)
D.
Over Lesson 5–2
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In ΔRST, RU is an altitude and SV is a median.
Find y if mRUS = 7y + 27.
A. 5
B. 7
C. 9
D. 11
Over Lesson 5–2
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In ΔRST, RU is an altitude and SV is a median.
Find RV if RV = 6a + 3 and RT = 10a + 14.
A. 3
B. 4
C. 21
D. 27
Over Lesson 5–2
Which of the following points is the center of
gravity of a triangle?
A. centroid
B. circumcenter
C. incenter
D. orthocenter
Content Standards
G.CO.10 Prove theorems about triangles.
Mathematical Practices
1 Make sense of problems and persevere in
solving them.
3 Construct viable arguments and critique
the reasoning of others.
You found the relationship between the angle
measures of a triangle.
• Recognize and apply properties of
inequalities to the measures of the angles of
a triangle.
• Recognize and apply properties of
inequalities to the relationships between the
angles and sides of a triangle.