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Chapter 4 – Congruent Triangles
4-1 Congruent Figures
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Objective: Recognize congruent figures and their corresponding parts.
DEF ≅ GHI
Vocabulary
are figures that have the same size and shape.
(DNG pages 72-74, text reference pages 198-200) 4-1 Congruent Figures
When you name congruent polygons, always list corresponding vertices in the same order.
Congruent polygons have congruent corresponding parts
Matching vertices are corresponding vertices.
Matching sides are corresponding sides.
Matching angles are corresponding angles.
Congruent polygons
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When two figures are congruent, you can move one so that it fits exactly on the other one.
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T C
180
QJ BC
mM
65
48
48 67
115
Examples
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Examples
ABC
DCE
DEC is not
DC DE EC
CDE DEC
ACB
EDC
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35
YSW K VM WYS MKV SWY VMK
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No, corresponding sides are not congruent.
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Practice 4-1 Congruent Figures
Each pair of polygons is congruent. Find the measures of the numbered angles.
CAT ≅ JSD. List each of the following.
4. three pairs of congruent sides
5. three pairs of congruent angles
m1 = 110, m2 = 120 m3 = 90, m4 = 135 m5 = 140, m6 = 90,
m7 = 40, m8 = 90
C ≅ J , A≅ S , T ≅ D
(DNG page 317)
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Practice 4-1 Congruent Figures
7. four pairs of congruent angles
6. four pairs of congruent sides
WXYZ ≅ JKLM. List each of the following.
State whether the pairs of figures are congruent. Explain.
W ≅ X X ≅ K Y ≅ L Z ≅ M
/
// //
////
GHJ ≅ IHJ
by Theorem 4-1
HJ ≅ HJ
by Reflexive Prop. of ≅,
GHJ ≅ IHJ
by the definition of ≅ triangles.
YES
X
RSQ ≅ VST
by Vertical s Theorem
QRS ≅ TSV
by Theorem 4-1
but none of the
sides are
necessarily ≅.
NO
(DNG page 317)
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Practice 4-1 Congruent Figures
10. Developing Proof Use the information given in the diagram.
Give a reason that each statement is true.
Given
Vertical Angles Theorem
Theorem 4-1
Given
Definition of ≅ Triangles
(DNG page 317)