Transcript Lesson 4-3 Congruent Triangles

Lesson 4-3 Congruent Triangles
• Congruent triangles- triangles that are the same
size and shape
• Definition of Congruent Triangles (CPCTC)
Two triangles are congruent if and only if their
corresponding sides are congruent.
• Congruence transformations- when you slide, flip,
or turn a triangle, the size and shapes do not
change.
Lesson 4-3 Congruent Triangles
• Theorem 4.4 Properties of Triangle
Congruence
• Reflexive
• Symmetric
• Transitive
ARCHITECTURE A tower roof is composed of congruent
triangles all converging
toward a point at the top. Name the corresponding congruent
angles
and sides of HIJ and LIK.
Answer: Since corresponding parts of congruent triangles are congruent,
ARCHITECTURE A tower roof is composed of congruent
triangles all converging
toward a point at the top.
Name the congruent triangles.
Answer: HIJ LIK
The support beams on the fence form congruent triangles.
a. Name the corresponding congruent angles
and sides of ABC and DEF.
Answer:
b. Name the congruent triangles.
Answer: ABC DEF
COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and
T(1, 1). The vertices of RST are R(3, 0), S(0, ─5), and T(─1, ─1). Verify
that
RST
RST.
Use the Distance Formula to find the length of each side of the triangles.
Use the Distance Formula to find the length of each side of the triangles.
Use the Distance Formula to find the length of each side of the triangles.
Answer: The lengths of the corresponding sides of two triangles are equal.
Therefore, by the definition of congruence,
Use a protractor to measure the angles of the triangles. You will find that the
measures are the same.
In conclusion, because
,
COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and
T(1, 1). The vertices of RST  are R(3, 0), S(0, ─5), and T(─1, ─1). Name
the congruence transformation for RST and RST.
Answer: RST is a turn of RST.
COORDINATE GEOMETRY The vertices of ABC are A(–5, 5), B(0, 3), and
C(–4, 1). The vertices of ABC are A(5, –5), B(0, –3), and C(4, –1).
a. Verify that ABC ABC.
Answer:
Use a protractor to verify that
corresponding angles are congruent.
b. Name the congruence transformation for ABC
and ABC.
Answer: turn