Download congruent triangles

CHAPTER 4:
CONGRUENT TRIANGLES
Section 4-1:
Congruent Figures
CONGRUENCE
• Congruent figures are two figures that
have the same size and shape.
• We are familiar with congruence involving
angles and segments.
• We will now apply congruence to triangles.
CONGRUENT TRIANGLES
Definition of congruent triangles:
Two triangles are congruent if and only if
their vertices can be matched up so that
corresponding parts of the triangles are
congruent.
CORRESPONDING PARTS OF
TRIANGLES
From the definition of congruent triangles,
corresponding parts consists of both
angles and sides of the triangles.
CONGRUENT TRIANGLES
Consider the following two triangles:
B
A
E
C
D
F
The following parts correspond:
• Vertices: A ↔ D, B ↔ E, C ↔ F
• Angles: A ↔ D, B ↔ E, C ↔ F
• Sides: AB ↔ DE, BC ↔ EF, AC ↔ DF
If the corresponding parts of triangles are
congruent, then the triangles are congruent.
CONGRUENT POLYGONS
Just as the case with triangles, two
polygons are congruent if and only if
their vertices can be matched up so that
their corresponding parts are congruent.
PRACTICE
1. An acute triangle is
________ congruent to
an obtuse triangle.
2. A polygon is ______
congruent to itself.
3. A right triangle is
______ congruent to
another right triangle.
4. If ABC ≡ XYZ, A is
_______ congruent to
Y.
5. If ABC ≡ XYZ, B is
_______ congruent to
Y.
1. Never
2. Always
3. Sometimes
4. Sometimes
5. Always
PRACTICE
Suppose TIM ≡ BER
Complete:
1. IM ≡ ___
1. ER
2. ___ ≡ R
2. M
3.
MTI ≡
___
3. RBE
PRACTICE
1. What definition underlies the statement:
“Corresponding parts of congruent
triangles are congruent”?
The definition of congruent triangles.
CLASSWORK/HOMEWORK
• Class work: Pg. 119, Classroom Exercises
2-20 Even.
• Home work: Pg. 120, Written Exercises 119 All.