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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
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.
Use the Exterior Angle Inequality Theorem
Use the Exterior Angle Inequality Theorem
By the Exterior Angle Inequality Theorem, m14 > m4
and m14 > m11. In addition, m14 > m2 and
m14 > m4 + m3, so m14 > m4 and m14 > m3.
Since 11 and 9 are vertical angles, they have
equal measure, so m14 > m9. m9 > m6 and
m9 > m7, so m14 > m6 and m14 > m7.
Use the Exterior Angle Inequality Theorem
Use the Exterior Angle Inequality Theorem
By the Exterior Angle Inequality Theorem, m10 > m5
and m16 > m10, so m16 > m5. Since 10 and
12 are vertical angles, m12 > m5. m15 > m12,
so m15 > m5. In addition, m17 > m5 + m6, so
m17 > m5.
A.
B.
C.
D.
A.
B.
C.
D.
Order Triangle Angle Measures
List the angles of ΔABC in order from smallest to
largest.
The sides from the shortest to longest are AB, BC, and
AC. The angles opposite these sides are C, A, and
B, respectively. So, according to the Angle-Side
Relationship, the angles from smallest to largest are
C, A, B.
Answer: C, A, B
List the angles of ΔTVX in
order from smallest to largest.
A. X, T, V
B. X, V, T
C. V, T, X
D. T, V, X
Order Triangle Side Lengths
List the sides of ΔABC in order from
shortest to longest.
The angles from smallest to largest are B, C, and A.
The sides opposite these angles are AC, AB, and BC,
respectively. So, the sides from shortest to longest are
AC, AB, BC.
Answer: AC, AB, BC
List the sides of ΔRST in order from
shortest to longest.
A. RS, RT, ST
B. RT, RS, ST
C. ST, RS, RT
D. RS, ST, RT
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?
Angle-Side Relationships
Theorem 5.10 states that if one side of a triangle is
longer than another side, then the angle opposite the
longer side has a greater measure than the angle
opposite the shorter side. Since X is opposite the
longest side, it has the greatest measure.
Answer: So, Ebony should tie the ends marked
Y and Z.
KITE ASSEMBLY Tanya is
following directions for making a
kite. She has two congruent
triangular pieces of fabric that
need to be sewn together along
their longest side. The directions
say to begin sewing the two pieces
of fabric together at their smallest angles. At which
two angles should she begin sewing?
A. A and D
B. B and F
C. C and E
D. A and B