Transcript 4-1 PPT Congruent Figures

Section 4-1 Congruent Figures
SPI 31A: identify corresponding parts of congruent geometric figures
SPI 32C: determine congruence or relations between triangles or
quadrilaterals given a diagram
Objectives:
• recognize congruent figures and their corresponding
parts
Congruent Polygons
Congruent Polygons have congruent corresponding parts
• Congruent sides
• Congruent Angles
• Matching vertices are corresponding vertices
• always list corresponding parts in the same order
Line AB  line DE
Line BC  line EF
Line CA  line FD
AD
BE
CF
E
B
D
A
C
F
Real-World Connection using Congruent Figures
The fins of the space shuttle suggest
congruent pentagons. Find the mB.
What is the angle corresponding to B? E
Use the Polygon Angle Sum Thm:
(n – 2)180 = (5 – 2)180 = 540
mS + mP + mA + mC + mE = 540
Angle Sum Thm
88 + 90 + 90 + 132 + mE = 540 Substitute
400 + mE = 540 Simplify
mE = 140 SPE
Since mB = mE, then angle B is 140
Are the Two Triangles Congruent?
Two triangles are congruent if they
have:
• 3 pairs of  corresponding sides
• 3 pairs of  corresponding angles
Look at the diagram. What do you know by the markings?
AC  EC
Given
AB  ED
 AB  3  ED
BC  DC
A  E
B  D
 BC  4  DC
Given
Right s are 
What is true about angles
ACB and DCE? Explain.
They are vertical angles,
so they are congruent.
Proving Triangle Congruency
Use the information in the diagram to give
a reason why each statement is true.
Statement
Reason
Given
PQ  PS , QR  SR
Reflexive Prop of 
PR  PR
Q  S , QPR  SPR Given
QRP  SRP
PQR  PSR
Theorem 4-1
Def of  triangles