Understand Congruent Figures

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Objectives

1.

Identify Corresponding Parts in Congruent Figures.

2.

Prove Triangles are Congruent.

4.2 Congruent Figures

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Definitions

Congruent figures have the exact same shape and
size. All the figures below are congruent. As shown
below, a flip, rotate (turn), or slide does not affect
whether figures are congruent because they still
have the same shape and size.

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Definitions

When figures are congruent, their corresponding
sides are congruent, and their corresponding angles
are congruent.

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Corresponding Angles
& Sides

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ExampleNaming Congruent Parts

For the two figures, we
are given that ABCD ≅TRQS.
Solution
The figures help, but having the congruent angles
listed in the corresponding order is all that is needed.
ABCD ≅TRQS
Angles:
Sides:

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Slide 4-5

Example
Using Congruent Triangles to

Find Angle Measures

In the process of folding an origami cat, two
congruent triangles are formed.
Given that ΔABC ≅ ΔAEF, |
find m∠F.
Solution
m∠C + 96° + 36° = 180°

m∠C = 48°

Since ΔABC ≅ ΔAEF,

m∠F = m∠C = 48°

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Theorem 4.2-1 Third Angles Theorem

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Example
Using the Third Angles Theorem

Find the value of x.
Solution
From the figures, we have
∠J ≅∠R and ∠H ≅∠S.
Thus, from the Third Angles Theorem,
∠K ≅∠Q or m∠K= m∠Q.
Use ΔJHK to find m∠K.
m∠K= 180° – 53° – 92° = 35°

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Example
Using the Third Angles Theorem

Find the value of x.
Solution
m∠K= m∠Q
35 = 10x + 5
30 = 10x
3 = x
The value of x is 3. To check, replace x with 3 and
see that 10x + 5 = 35. Then make sure that
53° + 92° + 35° = 180°.

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Slide 4-9

ExampleProving Triangles Are Congruent

Given: segments LM ≅LO, MN ≅ON,
∠M ≅∠O, ∠MLN ≅∠OLN
Prove: ΔLMN ≅ ΔLON

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Slide 4-10

ExampleProving Triangles Are Congruent

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Statements

Reasons

1. Given

2. Reflexive Property of Congruence

3. Given

4. Third Angles Theorem

5. Definition of congruent
triangles

Multiple Choice

Tell whether the two figures are congruent.

• Yes, same size and same shape
• No, same shape but different sizes
• No, different size and different shapes

Multiple Choice

Are these two shapes congruent or not congruent?

• congruent
• not congruent

Open Ended

If △ABC is congruent to △XYZ then complete following statement.

Line segment BC is congruent to line segment _______.

Open Ended

If △ABC is congruent to △XYZ then complete following statement.

Line segment XY measures _______.

Multiple Choice

Which side corresponds with

$$\overline{AC}$$ ?

• $$\overline{YZ}$$  

• $$\overline{AB}$$  
  

• $$\overline{XY}$$  
  

• $$\overline{XZ}$$  
  

Multiple Choice

Figures CMJXT and PDNER are congruent.
Which line segment in figure PDNER must be
congruent to $$\overline{JX}$$ ? 

• $$\overline{NE}$$  

• $$\overline{CT}$$  

• $$\overline{PR}$$  

• $$\overline{DP}$$  

Multiple Choice

Figures CMJXT and PDNER are congruent.
Which line segment in figure PDNER must be
congruent to $$\overline{RE}$$ ? 

• $$\overline{JT}$$  

• $$\overline{TC}$$  

• $$\overline{TX}$$  

• $$\overline{MX}$$  

Multiple Select

Which shapes are congruent to the figure (more than one)?