lesson: pages: objectives: 4.3 exploring congruent triangles 196 – 197 to name and label...
TRANSCRIPT
Lesson:
Pages:
Objectives:
4.3 Exploring CONGRUENT Triangles
196 – 197
To NAME and LABEL Corresponding PARTS of CONGRUENT Triangles
To STATE the CPCTC Theorem
• congruent triangles
• congruence transformations
GEOMETRY 4.3
Congruent Polygons have the:
SAME Size
SAME Shape
GEOMETRY 4.3
Congruent Polygons have the:
SAME Size
SAME Shape
Congruent TRIANGLES have
Congruent CORRESPONDING SIDES
Congruent CORRESPONDING Angles
GEOMETRY 4.3
Congruent TRIANGLES have
Congruent CORRESPONDING SIDES
Congruent CORRESPONDING Angles
A B
C
D E
F
GEOMETRY 4.3
Congruent TRIANGLES have
Congruent CORRESPONDING SIDES
Congruent CORRESPONDING Angles
A B
C DE
F
GEOMETRY 4.3
Congruent TRIANGLES have
Congruent CORRESPONDING SIDES
Congruent CORRESPONDING Angles
Because CORRESPONDING parts determine Congruence:
You may have to:
Slide Rotate, or Flip
Figures to determine whether they are CONGRUENT
GEOMETRY 4.3GEOMETRY 4.3
Congruent TRIANGLES have
Congruent CORRESPONDING SIDES
Congruent CORRESPONDING Angles
The way you NAME the Triangle establishes theCORRESPONDENCE:
GEOMETRY 4.3
To WRITE the CORRESPONDINGParts of Congruent Triangles,use
GEOMETRY 4.3
SO, if ABC FGH:
Congruent Angles Congruent Sides
GEOMETRY 4.3
Congruent Angles Congruent Sides
Be sure to WRITE the LETTERS of VERTICESin the CORRECT ORDER when you write a Statement.
SO, if ABC FGH:
GEOMETRY 4.3
A THEOREM:
Two Triangles are CONGRUENT
if and only if
Their CORRESPONDING PARTS are CONGRUENT
GEOMETRY 4.3
A THEOREM:
Two Triangles are CONGRUENT
if and only if
Their CORRESPONDING PARTS are CONGRUENT
This is called CPCTC
GEOMETRY 4.3
A THEOREM:
Two Triangles are CONGRUENT
if and only if
Their CORRESPONDING PARTS are CONGRUENT
This is called CPCTC(Corresponding Parts of Congruent Triangles are Congruent.)
GEOMETRY 4.3
Name the CORRESPONDING CONGRUENT Angles & Sides.
TRU TSU
GEOMETRY 4.3
CONGRUENCE of TRIANGLES is:
REFLEXIVE
SYMMETRIC, and
TRANSITIVE
A THEOREM:
GEOMETRY 4.3
CONGRUENCE of TRIANGLES is:
REFLEXIVE
SYMMETRIC, and
TRANSITIVE
A THEOREM:
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
B. COORDINATE GEOMETRY The vertices of ΔRST are R(–3, 0), S(0, 5), and T(1, 1). The vertices of ΔRST are R(3, 0), S(0, –5), and T(–1, –1). Use the Distance Formula to verify that corresponding sides are congruent. Name the congruence transformation for ΔRST and ΔRST.
GEOMETRY 4.3
You should be able to:
State the CPCTC Theorem
DESCRIBE how Triangle Congruence is Reflexive, Symmetric and Transitive
Use CPCTC in a Proof
DETERMINE if Corresponding Part of Triangles are Congruent.
GEOMETRY 4.4
Recall that CONGRUENCE means
o Same SHAPEo Same SIZE
GEOMETRY 4.4
Recall that CONGRUENCE means
o Same SHAPEo Same SIZE
Now for some SHORTCUT postulates and theoremsthat don’t require proving ALL Corresponding Angles and ALL Corresponding Sides are Congruent.
GEOMETRY 4.4
SSS Postulate
If the SIDES of one triangle are CONGRUENT to the SIDES of a Second Triangle,
THEN
the Triangles are CONGRUENT.
GEOMETRY 4.4
DEFINITION:
The Included Angle of Two Sides is the Angleformed by them.
A B
C
1
2
3
GEOMETRY 4.4
SAS Postulate
If TWO SIDES and the INCLUDED ANGLE of one Triangle are CONGRUENT to
TWO SIDES and the INCLUDED ANGLE of another Triangle
THEN
The Triangles are CONGRUENT.
GEOMETRY 4.4
GEOMETRY 4.4
GEOMETRY 4.4Which pair of Triangles are CONGRUENT?
GEOMETRY 4.4Which pair of Triangles are CONGRUENT?
GEOMETRY 4.4Which pair of Triangles are CONGRUENT?
GEOMETRY 4.4Which pair of Triangles are CONGRUENT?
GEOMETRY 4.4
GEOMETRY 4.4