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: 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. A B C D E F

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 1.IM ≡ ___ 2.___ ≡ R 3. MTI ≡ ___ 1.ER 2.M 3.RBE Suppose TIM ≡ BER Complete:

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 All.