NAME DATE PERIOD 4-3 Study Guide and Intervention

NAME

DATE

PERIOD

4-3 Study Guide and Intervention

Congruent Triangles

Congruence and Corresponding Parts

Triangles that have the same size and same shape are congruent triangles. Two triangles are congruent if and only if all three pairs of corresponding angles are congruent and all three pairs of corresponding sides are congruent. In the figure, ABC RST.

B

S

R

C

T

A

Third Angles Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 4-3

Example If XYZ RST, name the pairs of

Y

congruent angles and congruent sides.

S

X R, Y S, Z T X--Y -R-S, -X-Z R--T, -Y-Z -ST-

X

Z

R T

Exercises

Show that the polygons are congruent by identifying all congruent corresponding parts. Then write a congruence statement.

1.

K

B

J

L

A

C

A J; B K;

C L; -AB- -JK-; -B-C -K-L; -AC- -JL-

ABC

JKL

2.

B

D 3. K

L

A

C

A D; ABC DCB

ACB DBC; -AC- -B-D -AB- -D-C

ABC

DCB

J

M

J L; JKM LMK;

KMJ MKL; -K-J -M-L -K-L -M-J

JKM

LMK

4. F

GL

K

E

J

E J; F K;

G L; -E-F -JK-; -EG- -JL-; -FG- -K-L;

FGE

KLJ

Suppose ABC DEF

7. Find the value of x. 27.8 8. Find the value of y. 35

Chapter 4

5. B

D

6. R

U

S

A

C

T

A D;

R T;

ABC DCB;

RSU TSU;

ACB DBC;

-AB- -D-C; -AC- -D-B;

-B-C -C-B; ABC

DCB

RUS TUS;

-R-U -TU-; -R-S -TS-;

-SU- -SU-; RSU

TSU

&

#

75? 64.3

% (2y - 5)? 90.6

2x + y

65?

40?

"

96.6

$

'

19

Glencoe Geometry

NAME

4-3

DATE

PERIOD

Study Guide and Intervention (continued)

Congruent Triangles

Prove Triangles Congruent Two triangles are congruent if and only if their

corresponding parts are congruent. Corresponding parts include corresponding angles and corresponding sides. The phrase "if and only if" means that both the conditional and its converse are true. For triangles, we say, "Corresponding parts of congruent triangles are congruent," or CPCTC.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Example Write a two-column proof.

Given:

AB---BD--

C--B-, A--D- C--D-, bisects ABC.

BAD

BCD

$

#

%

Prove: ABD CBD

Proof:

"

Statement 1. A-B- C--B-, A--D- C--D- 2. B--D- B--D-

Reason 1. Given 2. Reflexive Property of congruence

3. BAD BCD

3. Given

4. ABD CBD

4. Definition of angle bisector

5. BDA BDC

5. Third Angles Theorem

6. ABD CBD

6. CPCTC

Exercises

Write a two-column proof.

1. Given: A-AC- biseCct, sB-D-D-. B, A--D- C--B-, A-E- C--E-, "

#

Prove: AED

Proof:

CEB

&

%

$

Statements

Reasons

1. A C, D B 1. Given

2. 3. 4.

AD--DEA--EDBC--E-B-,A-CE-EB

C-E-

2. Vertical angles are . 3. Given 4. Definition of segment bisector

5. AED CEB

5. CPCTC

Write a paragraph proof. 2. Given: BA---BD-- bisC-e-Bc-t,sA-B-ABCA--Da-n, dC--B-ADDC--C,-

#

Prove:

We are

ABD

given

B-D-CbBiDsects

ABC

and

ADC.

Therefore

ABD CBD and ADB CDB by the definition

"

$

Aaof-infnD-ddanCt-ghCB--laeD-t b.iFDA-sieCn-ca.tlUolyrsC,sinB..-gWBD-ytehtaehB-reseD-uTgbuhisvsirteidinntugAtthitnohagnetleApR-TrBe-ohfpleeeoxCr-ritveBy-em,, wPA,-rweB-oecpaenAr-tDyd-,eotfercmoninger%uthenatce.

Therefore ABD CBD by CPCTC.

Chapter 4

20

Glencoe Geometry

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