State the one to one correspondence
of the vertices of the congruent
quadrilaterals WXYZ and DEFG. Name
the pairs of congruent sides.
Answers
Answer:
Reflect
1. If you know that △ABC ≅ △DEF, what six congruence statements about
segments and angles can you write? Why?
2. Do your findings in this Explore apply to figures
other than triangles? For instance, if you know that
quadrilaterals JKLM and PQRS are congruent, can
you make any conclusions about corresponding
parts? Why or why not?
Explain 1 Corresponding Parts of Congruent Figures
Are Congruent
The following true statement summarizes what you discovered in the Explore.
Corresponding Parts of Congruent Figures Are Congruent
If two figures are congruent, then corresponding sides are congruent and
corresponding angles are congruent.
Example 1 △ABC ≅ △DEF. Find the given side length or angle measure.
DE
Step 1 Find the side that corresponds to _
DE .
Since △ABC ≅ △DEF,
_
AB ≅
_
DE .
Step 2 Find the unknown length.
DE = AB, and AB = 2.6 cm,
so DE = 2.6 cm.
m∠B
Step 1 Find the angle that corresponds to ∠B.
Since △ABC ≅ △DEF, ∠B ≅ ∠ .
Step 2 Find the unknown angle measure.
m∠B = m∠ , and m∠ = °, so m∠B = °.
L
K
M
J
R
Q
S
P
F E 42°
73°
65°
D
B C
A
2.6 cm
3.7 cm
3.5 cm
AB ¯≅ DE¯, ¯BC ≅ EF¯, ¯
AC ≅ DF¯, ∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F. The rigid motions that map
△ABC to △DEF also map the sides and angles of △ABC to the corresponding sides and
angles of △DEF, which establishes congruence.
Yes; since quadrilateral JKLM is congruent to quadrilateral PQRS, there is a sequence of
rigid motions that maps JKLM to