Right Triangle Congruence Theorems

Lesson 6.1

Skills Practice

Name

Date

Time to Get Right

Right Triangle Congruence Theorems

Vocabulary

Choose the diagram that models each right triangle congruence theorem.

1. Hypotenuse-Leg (HL) Congruence Theorem

a.

X

Y

R

b

Q

P

Z

2. Leg-Leg (LL) Congruence Theorem

b.

U

V

W

d

X

3. Hypotenuse-Angle (HA) Congruence Theorem ???? c.

E

F

a

? Carnegie Learning

G

I

4. Leg-Angle (LA) Congruence Theorem

H

d.

6

W

T

c

U

X

V

Y

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Lesson 6.1

Skills Practice

page 2

Problem Set

Mark the appropriate sides to make each congruence statement true by the Hypotenuse?Leg

Congruence Theorem.

1. «±DPR ªß «±QFM

R

2. «±ACI ªß «±GCE

A

M

I

C

F

D

E

Q

P

G

3. «±QTR ªß «±SRT

T

4. «±ADG ªß «±HKN

Q

D

A

S

N

K

R

H

G

Mark the appropriate sides to make each congruence statement true by the Leg?Leg

Congruence Theorem.

5. «±BZN ªß «±TGC

6. «±MNO ªß «±QPO

G

T

N

P

B

O

6

Z

C

7. «±PZT ªß «±PZX

M

Q

8. «±EGI ªß «±ONQ

P

E

G

N

I

Q

O

T

Z

X

588

Chapter 6 Skills Practice

? Carnegie Learning

N

Lesson 6.1

Skills Practice

page 3

Name

Date

Mark the appropriate sides and angles to make each congruence statement true by the

Hypotenuse?Angle Congruence Theorem.

9. «±SVM ªß «±JFW

10. «±MSN ªß «±QRT

W

F

V

P

J

S

N

T

M

S

11. «±IEG ªß «±IEK

M

Q

R

12. «±DCB ªß «±ZYX

E

G

Y

D

B

I

X

K

C

Z

Mark the appropriate sides and angles to make each congruence statement true by the Leg?Angle

Congruence Theorem.

13. «±XTD ªß «±HPR

14. «±SEC ªß «±PEC

P

X

T

S

R

? Carnegie Learning

T

C

D

D

E

6

H

P

R

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Lesson 6.1

Skills Practice

15. «±PBJ ªß «±OTN

page 4

16. «±AXT ªß «±YBU

P

A

X

B

Y

B

J

T

O

T

U

N

For each figure, determine if there is enough information to prove that the two triangles are congruent.

If so, name the congruence theorem used.

___

___

___

17. Given: GF

? ?bisects /RGS, and

18. Given: DV

? ?ªÈ TU

? ?

/R and /S are right angles. Is nDVT > nDVU?

Is nFRG > nFSG?

G

D

S

R

T

V

U

F

 es. There is enough information

Y

to conclude that nFRG > nFSG

by HA.

____

____ ____

No. nDVT might not be

?? congruent to nDVU. There is

?? not enough information.

____

___

___

19. Given: NM

? ?> EM

? ?, DM

? ?> OM

? ?, and

20. Given: RP

? ?> QS

? ?, and /R and /Q

/NMD and /EMO are right angles. are right angles.

N

O

6

M

E

Chapter 6 Skills Practice

S

P

Q

D

 es. There is enough information to

Y

conclude that nNMD > nEMO by LL.

590

R

Yes. There is enough information to

?? conclude that nSRP > nPQS by HL.

? Carnegie Learning

Is nNMD > nEMO? Is nSRP > nPQS?

Lesson 6.1

Skills Practice

page 5

Name

Date

____

____

___

____

21. Given: GO

? ?> MI

? ?, and /E and /K are

22. Given: HM

? ?> VM

? ?, and /H and /V are

right angles. right angles.

Is nGEO > nMKI? Is nGHM > nUVM?

E

G

I

G

H

M

O

M

K

V

U

 o. nGEO might not be congruent to

N

nMKI. There is not enough information.

Yes. There is enough information to

?? conclude that nGHM > nUVM by LA.

Use the given information to answer each question.

23. T

 wo friends are meeting at the library. Maria leaves her house and walks north on Elm Street and then

east on Main Street to reach the library. Paula leaves her house and walks south on Park Avenue and

then west on Main Street to reach the library. Maria walks the same distance on Elm Street as Paula

walks on Main Street, and she walks the same distance on Main Street as Paula walks on Park

Avenue. Is there enough information to determine whether Maria¡¯s walking distance is the same as

Paula¡¯s walking distance?

Paula¡¯s house

Park Avenue

N

W

E

S

Elm Street

? Carnegie Learning

Main Street

Library

Maria¡¯s house

Yes. Maria¡¯s walking distance to the library is equal to Paula¡¯s walking distance. The triangles

formed are right triangles. The corresponding legs of the triangles are congruent. So, by the

Leg-Leg Congruence Theorem, the triangles are congruent. If the triangles are congruent, the

hypotenuses are congruent.

Chapter 6 Skills Practice

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