# Lesson: Pages: Objectives: 4.3 Exploring CONGRUENT Triangles 196 – 197  To NAME and LABEL Corresponding PARTS of CONGRUENT Triangles  To STATE the CPCTC.

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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 DE 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 4.3 Congruent TRIANGLES have Congruent CORRESPONDING SIDES Congruent CORRESPONDING Angles The way you NAME the Triangle establishes the CORRESPONDENCE:

GEOMETRY 4.3 To WRITE the CORRESPONDING Parts of Congruent Triangles, use

GEOMETRY 4.3 SO, if ABC  FGH: Congruent AnglesCongruent Sides

GEOMETRY 4.3 Congruent AnglesCongruent Sides Be sure to WRITE the LETTERS of VERTICES in 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

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 SHAPE o Same SIZE

GEOMETRY 4.4 Recall that CONGRUENCE means o Same SHAPE o Same SIZE Now for some SHORTCUT postulates and theorems that 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 Angle formed by them. AB 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

Which pair of Triangles are CONGRUENT?

GEOMETRY 4.4 Which pair of Triangles are CONGRUENT?

GEOMETRY 4.4 Which pair of Triangles are CONGRUENT?

GEOMETRY 4.4 Which pair of Triangles are CONGRUENT?

GEOMETRY 4.4

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