4.2 congruence of triangles (reflexive, symetric, transitive)

8/13/2019 4.2 Congruence of Triangles (Reflexive, Symetric, Transitive)

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4 3Congruent TrianglesWe will

name and label corresponding parts of

congruent triangles.identify congruence transformations.


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Corresponding parts

of congruent triangles

Triangles that are the same size and shape

are congruent triangles.

Each triangle has three angles and three

sides. If all six corresponding parts are

congruent, then the triangles are

congruent.


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Corresponding parts


A

C

B

X

Z

Y

IfABCis congruent toXYZ , then vertices of the two triangles

correspond in the same order as the letter naming the triangles.

ABC=XYZ~


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Corresponding parts


A

C

B

X

Z

Y

This correspondence of vertices can be used to name thecorresponding congruent sides and angles of the two triangles.

ABC=XYZ~


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Definition of CongruentTriangles CPCTC)Two triangles are congruent if and

only if their corresponding partsare congruent.CPCTCCorresponding Parts of CongruentTriangles are Congruent


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Answer:Since corresponding parts of congruent trianglesare congruent,

ARCHITECTURE A tower roof is composed ofcongruent triangles all convergingtoward a point at the top. Name thecorresponding congruent anglesand sides of HIJand LIK.


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Answer:

The support beams on the fence form congruenttriangles.

b.Name the congruent triangles.

a.Name the correspondingcongruent angles and sides ofABCand DEF.

Answer: ABC DEF


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Properties of TriangleCongruenceCongruence of triangles is reflexive,symmetric, and transitive.

REFLEXIVEK

J

L

K

J

LJKL = JKL~


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Properties of TriangleCongruenceCongruence of triangles is reflexive,symmetric, and transitive.SYMMETRIC

K

J

L

Q

P

RIfJKL = PQR,

thenPQR =JKL.

~

~


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Properties of TriangleCongruenceCongruence of triangles is reflexive,symmetric, and transitive.TRANSITIVE

K

J

L

Q

P

R

IfJKL = PQR, and

PQR = XYZ, then

JKL =XYZ.

~

~

~

Y

X

Z


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IDENTIFY CONGRUENCE

TRANSFORMATIONS

B

A

C

B

A

C

If you slideABC down and to the

right, it is still congruent toDEF.

E

D

F


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IDENTIFY CONGRUENCE

TRANSFORMATIONS

B

A

C B

A

C

If you turnABC,

it is still congruent toDEF.

E

D

F


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IDENTIFY CONGRUENCE

TRANSFORMATIONS

B

A

C

B

A

C

If you flipABC,

it is still congruent toDEF.

E

D

F


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COORDINATE GEOMETRY The vertices of RSTareR(3, 0), S(0, 5),and T(1, 1).The vertices of RSTare R(3, 0), S(0,5),and T(1, 1).Verify that

RST RST.


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Use the Distance Formula to find the length of each side ofthe triangles.


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Use a protractor to measure the angles of the triangles. Youwill find that the measures are the same.

Answer: The lengths of the corresponding sides of twotriangles are equal. Therefore, by the definitionof congruence,

In conclusion, because ,


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COORDINATE GEOMETRY The vertices of RSTareR(3, 0), S(0, 5),and T(1, 1).The vertices of RST are R(3, 0), S(0,5),and T(1, 1). Name thecongruence transformation for RSTand RST.

Answer:RSTis aturn of RST.


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COORDINATE GEOMETRY The vertices of ABC areA(5, 5), B(0, 3),and C(4, 1).The vertices of ABCareA(5,5), B(0,3),and C(4,1).

Answer:

Use a protractor to verify thatcorresponding angles arecongruent.

a. Verify that ABC ABC.


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Answer:turn

b.Name the congruence transformation for ABCand ABC.


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BOOKWORK:

p. 195 #919,

#2225 (just name the congruence transformation)

HOMEWORK:

p.198 Practice Quiz

4.2 congruence of triangles (reflexive, symetric, transitive)

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