Download 4-2 - Midland ISD

LESSON 4–2
Angles of Triangles
Five-Minute Check (over Lesson 4–1)
TEKS
Then/Now
New Vocabulary
Theorem 4.1: Triangle Angle-Sum Theorem
Proof: Triangle Angle-Sum Theorem
Example 1: Real-World Example: Use the Triangle Angle-Sum
Theorem
Theorem 4.2: Exterior Angle Theorem
Proof: Exterior Angle Theorem
Example 2: Real-World Example: Use the Exterior Angle Theorem
Corollaries: Triangle Angle-Sum Corollaries
Example 3: Find Angle Measures in Right Triangles
Over Lesson 4–1
Classify ΔRST .
A. acute
B. equiangular
C. obtuse
D. right
Over Lesson 4–1
Find
y___
if ΔRST is an isosceles triangle with
___
RS  RT.
A. 8
B. 10
C. 12
D. 14
Over Lesson 4–1
Find x if ΔABC is an equilateral
triangle.
A. 2
B. 4
C. 6
D. 8
Over Lesson 4–1
A. ΔABC
B. ΔACB
C. ΔADC
D. ΔCAB
Over Lesson 4–1
Classify ΔMNO as scalene, isosceles, or equilateral
if MN = 12, NO = 9, and MO = 15.
A. scalene
B. isosceles
C. equilateral
Over Lesson 4–1
Which is not a classification for ΔFGH?
A.
acute
B.
scalene
C.
isosceles
D.
equiangular
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(D), G.1(F)
You classified triangles by their side or angle
measures.
• Apply the Triangle Angle-Sum Theorem.
• Apply the Exterior Angle Theorem.
• auxiliary line
• exterior angle
• remote interior angles
• flow proof
• corollary
Use the Triangle Angle-Sum
Theorem
SOFTBALL The diagram
shows the path of the
softball in a drill developed
by four players. Find the
measure of each numbered
angle.
Analyze
Examine the information in the diagram.
You know the measures of two angles of
one triangle and only one measure of
another. You also know that 1 and 2
are vertical angles.
Use the Triangle Angle-Sum
Theorem
Formulate
Find m1 first because the measure of
two angles of the triangle are known.
Use the Vertical Angles Theorem to find
m2. Then you will have enough
information to find the measure of 3.
Determine
Triangle Angle-Sum Theorem
Simplify.
Subtract 117 from each side.
Use the Triangle Angle-Sum
Theorem
1 and 2 are congruent vertical angles. So, m2 = 63.
Triangle Angle-Sum Theorem
Simplify.
Subtract 142 from each side.
Answer: Therefore, m1 = 63, m2 = 63, and
m3 = 38.
Justify
The sums of the measures of the angles in
each triangle should be 180.
m1 + 43 + 74 = 63 + 43 + 74 or 180
m2 + m3 + 79 = 63 + 38 + 79 or 180
Use the Triangle Angle-Sum
Theorem
Evaluate
By identifying each part of the problem, this
complex problem could be separated into three
manageable pieces. The properties of triangles were
used to check the reasonableness of the answers found.
Find the measure of 3.
A. 95
B. 75
C. 57
D. 85
Use the Exterior Angle Theorem
GARDENING Find the measure
of FLW in the fenced flower
garden shown.
mLOW + mOWL = mFLW
x + 32 = 2x – 48
Exterior Angle
Theorem
Substitution
32 = x – 48
Subtract x from
each side.
80 = x
Add 48 to each side.
Answer: So, mFLW = 2(80) – 48 or 112.
The piece of quilt fabric is in the shape of a right
triangle. Find the measure of ACD.
A. 30
B. 40
C. 50
D. 130
Find Angle Measures in Right Triangles
Find the measure of
each numbered angle.
Exterior Angle Theorem
m1 = 38 + 32
Simplify.
= 70
70 + m2 = 180
110
If 2 s form a linear pair, they
are supplementary.
Substitution
Subtract 70 from each side.
Find Angle Measures in Right Triangles
m 3 + 64 = 110
Exterior Angle Theorem
Simplify.
= 46
If 3 s form a linear pair,
they are supplementary
46+ 32+ m 4 = 180
78+ m4 = 180
102
Simplify.
Subtract 78 from each
side.
Find Angle Measures in Right Triangles
m5 + 102+ 41 = 180
m5 + 143 = 180
37
Triangle Angle-Sum Theorem
Simplify.
Subtract 143 from each side.
m1 = 70, m2 = 110, m3 = 46,
m4 = 102, m5 =37
Find m3.
A. 50
B. 45
C. 85
D. 130
LESSON 4–2
Angles of Triangles