lesson 4.3

download report

Transcript lesson 4.3

Five-Minute Check (over Lesson 4–2)
NGSSS
Then/Now
New Vocabulary
Key Concept: Definition of Congruent Polygons
Example 1: Identify Corresponding Congruent Parts
Example 2: Use Corresponding Parts of Congruent Triangles
Theorem 4.3: Third Angles Theorem
Example 3: Real-World Example: Use the Third Angles
Theorem
Example 4: Prove that Two Triangles are Congruent
Theorem 4.4: Properties of Triangle Congruence
Over Lesson 4–2
Find m1.
A. 115
B. 105
C. 75
D. 65
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
Find m2.
A. 75
B. 72
C. 57
D. 40
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
Find m3.
A. 75
B. 72
C. 57
D. 40
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
Find m4.
A. 18
B. 28
C. 50
D. 75
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
Find m5.
A. 70
B. 90
C. 122
D. 140
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
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
0%
B
D. 100
A
0%
A
B
C
0%
D
D
C. 50
A.
B.
C.
0%
D.
C
B. 40
MA.912.G.4.4 Use properties of congruent
and similar triangles to solve problems
involving lengths and areas.
MA.912.G.4.6 Prove that triangles are
congruent or similar and use the concept of
corresponding parts of congruent triangles.
You identified and used congruent angles.
(Lesson 1–4)
• 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: 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 directly matches
corresponding angles or sides?
A.
A.
B.
C.
D.
B.
C.
D.
0%
D
0%
C
0%
B
A
0%
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: 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
0%
B
A
0%
A
B
C
0%
D
D
D. x = 4.5, y = 5.5
C
C. x = 1.8, y = 19
A.
B.
C.
0%
D.
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 J  K
and mJ = 72, find mJIH.
∆JIK  ∆JIH
mKJI + mIKJ +
mJIK
= 180
H  K, I  I, and J  J
Congruent Triangles
Triangle Angle
Sum Theorem
CPCTC
Use the Third Angles Theorem
72 + 72 + mJIK = 180
144 + mJIK = 180
Substitution
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 ∆KLM  ∆NJL, KLM  KML and mKML = 47.5,
find mLNJ.
A. 85
B. 45
C. 47.5
0%
D
0%
C
A
0%
B
0%
D. 95
A.
B.
C.
D.
A
B
C
D
Prove That Two Triangles are Congruent
Write a two-column proof.
Prove: ΔLMN  ΔPON
Prove That Two Triangles are Congruent
Proof:
Statements
Reasons
1.
1. Given
2. LNM  PNO
2. Vertical Angles Theorem
3. M  O
3. Third Angles Theorem
4. ΔLMN  ΔPON
4. CPCTC
Find the missing information in the following proof.
Prove: ΔQNP  ΔOPN
Proof:
Statements
Reasons
1.
1. Given
2.
3.Q  O, NPQ  PNO
4. QNP  ONP
2. Reflexive Property of
Congruence
3. Given
4. _________________
?
5. ΔQNP  ΔOPN
5. Definition of Congruent Polygons
A. CPCTC
B. Vertical Angles Theorem
C. Third Angle Theorem
A
B
C
0%
D
D
0%
B
A
0%
C
D. Definition of Congruent
Angles
A.
B.
C.
0%
D.