Transcript B - Spring Branch ISD

LESSON 5–3
Inequalities in One
Triangle
Five-Minute Check (over Lesson 5–2)
TEKS
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
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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
Targeted TEKS
G.6(D) Verify theorems about the
relationships in triangles, including proof
of the Pythagorean Theorem, the sum of
interior angles, base angles of isosceles
triangles, midsegments, and medians, and
apply these relationships to solve problems.
Mathematical Processes
G.1(E), G.1(F)
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.
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
LESSON 5–3
Inequalities in One
Triangle