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Splash Screen. Five-Minute Check (over Lesson 4–2) CCSS 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

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Splash screen

Splash Screen


Lesson menu

Five-Minute Check (over Lesson 4–2)

CCSS

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

Lesson Menu


5 minute check 1

Find m1.

A.115

B.105

C.75

D.65

5-Minute Check 1


5 minute check 2

Find m2.

A.75

B.72

C.57

D.40

5-Minute Check 2


5 minute check 3

Find m3.

A.75

B.72

C.57

D.40

5-Minute Check 3


5 minute check 4

Find m4.

A.18

B.28

C.50

D.75

5-Minute Check 4


5 minute check 5

Find m5.

A.70

B.90

C.122

D.140

5-Minute Check 5


5 minute check 6

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

5-Minute Check 6


Splash screen

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.

CCSS


Then now

You identified and used congruent angles.

  • Name and use corresponding parts of congruent polygons.

  • Prove triangles congruent using the definition of congruence.

Then/Now


Vocabulary

  • congruent

  • congruent polygons

  • corresponding parts

Vocabulary


Concept 1

Concept 1


Example 1

Angles:

Sides:

Identify Corresponding Congruent Parts

Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.

Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ.

Example 1


Example 11

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?

Example 1


Example 2

Use Corresponding Parts of Congruent Triangles

In the diagram, ΔITP ΔNGO. Find the values of x and y.

OPCPCTC

mO=mPDefinition of congruence

6y – 14=40Substitution

Example 2


Example 21

CPCTC

Use Corresponding Parts of Congruent Triangles

6y=54Add 14 to each side.

y=9Divide each side by 6.

NG=ITDefinition of congruence

x – 2y=7.5Substitution

x – 2(9)=7.5y = 9

x – 18=7.5Simplify.

x=25.5Add 18 to each side.

Answer:x = 25.5, y = 9

Example 2


Example 22

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

Example 2


Concept 2

Concept 2


Example 3

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=180Triangle Angle-SumTheorem

Example 3


Example 31

Use the Third Angles Theorem

mIJK + mIJK + mJIK =180Substitution

72 + 72 + mJIK =180Substitution

144 + mJIK =180Simplify.

mJIK =36Subtract 144 fromeach side.

mJIH =36Third Angles Theorem

Answer:mJIH = 36

Example 3


Example 32

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

Example 3


Example 4

Prove That Two Triangles are Congruent

Write a two-column proof.

Prove:ΔLMNΔPON

Example 4


Example 41

StatementsReasons

1. Given

1.

2. LNM  PNO

2. Vertical Angles Theorem

3.M  O

3. Third Angles Theorem

4.ΔLMNΔPON

4. CPCTC

Prove That Two Triangles are Congruent

Proof:

Example 4


Example 42

Statements

Reasons

1. Given

1.

2. Reflexive Property ofCongruence

2.

3.Q  O, NPQ  PNO

3. Given

4. _________________

4.QNP  ONP

?

5.ΔQNPΔOPN

5. Definition of Congruent Polygons

Find the missing information in the following proof.

Prove:ΔQNPΔOPN

Proof:

Example 4


Example 43

A.CPCTC

B.Vertical Angles Theorem

C.Third Angles Theorem

D.Definition of Congruent Angles

Example 4


Concept 3

Concept 3


End of the lesson

End of the Lesson


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