Download Ch 4.1 Congruent Figures

4.1 Congruent Figures
Essential Question:
How do you recognize congruent figures and their
corresponding parts?
• Congruent figures: same size and shape.
– When two figures are congruent, you can move
one so that it fits exactly on the other one.
• Congruent polygons: congruent
corresponding parts.
– Matching sides and angles
– Matching vertices are corresponding vertices.
• When you name congruent polygons, always
list corresponding vertices in the same order.
Practice
• List the congruent corresponding sides and
angles given that ΔABC ≅ ΔDEF.
A
E
C
B
D
F
Practice
• Given that ΔWYS ≅ ΔMKV. If m<Y = 35, what is
m<K? Explain.
• Given ΔXYW ≅ ΔHIJ, how would you draw
these triangles?
Finding Congruent Triangles
• Decide whether the triangles are congruent.
Justify your answer.
E
76°
3
B
4
90°
3
76°
A
90°
C
4
D
• Theorem 4-1
– If two angles of one triangle are congruent to two
angles of another triangle, then the third angles
are congruent.
E
Ex: <C ≅ <F A
D
C
B
F
Proving Triangles Congruent
• Given: PQ ≅ PS, QR ≅ SR, <Q ≅ <S, <QPR ≅ <SPR
• Prove: ΔPQR ≅ ΔPSR
P
Statements
Reasons
Q
78 78°
°
R
S
Summary
• Answer the essential question in complete
sentences.
– How do you recognize congruent figures and
their corresponding parts?
• Write 2-4 study questions in the left column
to correspond to the notes.