4-1 Congruent Figures
Congruent Polygons
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Congruent figures have the same size and shape
They should fit exactly on top of each other if moved
You can move them by making a slide, flip or turn.
Congruent Polygons: have congruent corresponding
parts– their matching sides and angles.
• matching vertices are corresponding vertices
• When naming congruent polygons, always list
corresponding vertices in the same order.
• Reflexive Property: anything is equal to itself!!!
Congruent Polygons
Example 1
Sides:
𝑻𝑫 ≅ 𝑹𝑭
𝑱𝑫 ≅ 𝑪𝑭
𝑻𝑱 ≅ 𝑹𝑪
Angles:
∠𝐓 ≅ ∠𝑹
∠𝐉 ≅ ∠𝐂
∠𝐃 ≅ ∠𝐅
Example 2
The two pentagons
are congruent,
find the measure
of ∠B.
Example 3
• Decide whether the triangles are congruent. Justify your
answer by developing the proof.
Statement
Reasons
1. GIVEN
2. GIVEN
3. GIVEN
4. GIVEN
5. Def. of Right Angles
6. Vertical Angles Thm
Theorem
Example 4
• Use the info given in the diagram. Give a reason
why each statement is true.
1. Given
2. Reflexive Prop.
3. Given
4. Thm. 4.1
5. Def. of Congruent
Polygons
On Your Own
• Show how you can conclude that the triangles
are congruent. List statements and reasons as
in example 4.
On Your Own
Statements
1. ∠𝐴 ≅ ∠𝐷; ∠𝐸 ≅ ∠𝐶
2. ∠𝐴𝐸𝐵 ≅ ∠DBC
3. 𝐴𝐸 ≅ 𝐷𝐶; 𝐸𝐵 ≅ 𝐶𝐵;
𝐵𝐴 ≅ 𝐵𝐷
4. ∆𝐴𝐸𝐵 ≅ ∆DCB
Reasons
1. Given
2. Vertical Angles Thm (or Thm. 4.1)
3. Given
4. Def. of Congruent Polygons
Practice
• Pg 182-183 # 3-13, 16-23, 24-28, 30-31, 38-40