Download + m - cloudfront.net

Over Lesson 4–2
Find m∠1.
A. 115
B. 105
C. 75
D. 65
Over Lesson 4–2
Find m∠1.
A. 115
B. 105
C. 75
D. 65
Over Lesson 4–2
Find m∠2.
A. 75
B. 72
C. 57
D. 40
Over Lesson 4–2
Find m∠2.
A. 75
B. 72
C. 57
D. 40
Over Lesson 4–2
Find m∠3.
A. 75
B. 72
C. 57
D. 40
Over Lesson 4–2
Find m∠3.
A. 75
B. 72
C. 57
D. 40
Over Lesson 4–2
Find m∠4.
A. 18
B. 28
C. 50
D. 75
Over Lesson 4–2
Find m∠4.
A. 18
B. 28
C. 50
D. 75
Over Lesson 4–2
Find m∠5.
A. 70
B. 90
C. 122
D. 140
Over Lesson 4–2
Find m∠5.
A. 70
B. 90
C. 122
D. 140
Over Lesson 4–2
One angle in an isosceles triangle has a measure of
80°. What is the measure of one of the other two
angles?
A. 35
B. 40
C. 50
D. 100
Over Lesson 4–2
One angle in an isosceles triangle has a measure of
80°. What is the measure of one of the other two
angles?
A. 35
B. 40
C. 50
D. 100
Content Standards
G.CO.7 Use the definition of congruence in terms of
rigid motions to show that two triangles are
congruent if and only if corresponding pairs of sides
and corresponding pairs of angles are congruent.
G.SRT.5 Use congruence and similarity criteria for
triangles to solve problems and to prove
relationships in geometric figures.
Mathematical Practices
6 Attend to precision.
3 Construct viable arguments and critique the
reasoning of others.
You identified and used congruent angles.
• Name and use corresponding parts of
congruent polygons.
• Prove triangles congruent using the
definition of congruence.
• congruent
• congruent polygons
• corresponding parts
Identify Corresponding Congruent Parts
Show that the polygons are
congruent by identifying all of
the congruent corresponding
parts. Then write a
congruence statement.
Angles:
Sides:
Answer:
Identify Corresponding Congruent Parts
Show that the polygons are
congruent by identifying all of
the congruent corresponding
parts. Then write a
congruence statement.
Angles:
Sides:
Answer: All corresponding parts of the two polygons
are congruent. Therefore, ABCDE ≅ RTPSQ.
The support beams on the fence form congruent
triangles. In the figure ΔABC ≅ ΔDEF, which of the
following congruence statements correctly
identifies corresponding angles or sides?
A.
B.
C.
D.
The support beams on the fence form congruent
triangles. In the figure ΔABC ≅ ΔDEF, which of the
following congruence statements correctly
identifies corresponding angles or sides?
A.
B.
C.
D.
Use Corresponding Parts of Congruent
Triangles
In the diagram, ΔITP ≅ ΔNGO. Find the values of
x and y.
∠O ≅ ∠P
m∠O = m∠P
6y – 14 = 40
CPCTC
Definition of congruence
Substitution
Use Corresponding Parts of Congruent
Triangles
6y = 54
y= 9
Add 14 to each side.
Divide each side by 6.
CPCTC
NG = IT
x – 2y = 7.5
x – 2(9) = 7.5
x – 18 = 7.5
x = 25.5
Answer:
Definition of congruence
Substitution
y=9
Simplify.
Add 18 to each side.
Use Corresponding Parts of Congruent
Triangles
6y = 54
y= 9
Add 14 to each side.
Divide each side by 6.
CPCTC
NG = IT
x – 2y = 7.5
x – 2(9) = 7.5
x – 18 = 7.5
x = 25.5
Answer: x = 25.5, y = 9
Definition of congruence
Substitution
y=9
Simplify.
Add 18 to each side.
In the diagram, ΔFHJ  ΔHFG. Find the values of
x and y.
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5
In the diagram, ΔFHJ  ΔHFG. Find the values of
x and y.
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5
Use the Third Angles Theorem
ARCHITECTURE A drawing of a
tower’s roof is composed of
congruent triangles all converging at
a point at the top. If ∠IJK ≅∠IKJ and
m∠IJK = 72, find m∠JIH.
ΔJIK ≅ ΔJIH Congruent Triangles
m∠IJK + m∠IKJ + m∠JIK =180
Triangle Angle-Sum
Theorem
Use the Third Angles Theorem
m∠IJK + m∠IJK + m∠JIK = 180
Substitution
72 + 72 + m∠JIK = 180
Substitution
144 + m∠JIK = 180
Answer:
Simplify.
m∠JIK = 36
Subtract 144 from
each side.
m∠JIH = 36
Third Angles
Theorem
Use the Third Angles Theorem
m∠IJK + m∠IJK + m∠JIK = 180
Substitution
72 + 72 + m∠JIK = 180
Substitution
144 + m∠JIK = 180
Simplify.
m∠JIK = 36
Subtract 144 from
each side.
m∠JIH = 36
Third Angles
Theorem
Answer: m∠JIH = 36
TILES A drawing of a tile contains a series of triangles,
rectangles, squares, and a circle.
If ΔKLM ≅ ΔNJL, ∠KLM ≅∠KML, and m∠KML = 47.5,
find m∠LNJ.
A. 85
B. 45
C. 47.5
D. 95
TILES A drawing of a tile contains a series of
triangles, rectangles, squares, and a circle.
If ΔKLM ≅ ΔNJL, ∠KLM ≅∠KML, and m∠KML = 47.5,
find m∠LNJ.
A. 85
B. 45
C. 47.5
D. 95
Prove That Two Triangles are Congruent
Write a two-column proof.
Prove: ΔLMN ≅ ΔPON
To be completed in class…...