35

5.6 pgs. 269-276 EQ: How can we prove triangle congruence using AAS? Date:

Explore: Glue your patty paper here:

1. Trace segment on your patty paper.

2. Use one end of the segment as the vertex for the given angle A. 3. Now place �C with one ray overlapping �A, so that the other ray will intersect point B if extended. Close the triangle.

4. Compare your triangle to your neighbor's. Are they the same? Would it have been possible to use the segment and angles given to create a different triangle?

Angle-Angle-Side (AAS) Theorem

If two ________________ and the non-included ______________ of two triangles are congruent,

then the triangles are congruent.

Example: Triangle Congruence Statements with Angle-Angle-Side a) b) c) d)

Example: Angle Bisectors in a ∆ ≅ Proof

Given: �K ≅ �D, � is bisected by

Prove: 'WKT ≅ 'WDT

A B

A

C

W

K

D

T

A

C

W

P N

H

F

Y

E

V

C

P

M

K

Z

X

R

H

Statements Reasons Given

Given

∠ ≅ ∠_________

_______ ≅

'WKT ≅ 'WDT

angles side

ol Fk Fkalternate

intEyes reflexivePOC because

parallelline

pears

4D aa

SPKMESPKZSCWAEDPHNSYFEESUFCSXHRESBR.lt

KELDFTbisectsLKWD

DWT DefofLBisectorNg I TW Reflexive POC

AAS DE th

36

Triangle Congruence Practice by

SSS, SAS, ASA, or AAS Determine whether the triangles are congruent by SSS, SAS, ASA, or AAS. Give a triangle congruency statement in corresponding order and justify your reasoning.

1. 2. 3.

4. 5. 6.

Add congruency marks for any sides and angles allowed, then decide whether the following sets of triangles are congruent by SSS, SAS, ASA, or AAS. Then give the triangle congruency statement in corresponding order and justify your reasoning.

7. 8. 9.

10. 11. 12.

J

N

C

R

E

D

B

M T

B A

P

W D

H

G

P

X

K

B M

T

M W

C

T

Z

N B

X

F A

C

H

M

T

R

W Z

E

C Z

E

P

H

A

B

H

O

W

D

X

D

R Y

Name _______________________________

Date _________________ Per ___________ HW #48

1 15 113

SAS S2EWESBTM

it

SAS

SINCEDQNC

37

13. Given: ≅ , � is bisected by

Prove: 'HTC ≅ 'STC

14. 'HAW # 'UDJ. Find x and y. Then find the measure of every angle. Show your work.

15. A triangle has angle measures such that the measure of angle C is twelve less than angle B, and angle A is four more than twice angle B. Find the measures of the angles. (Hint: Draw a picture.) Show your work.

For the following triangles, find x and justify your work.

16. 17.

5x°

H

W (4y + 30)°

A

C

T

H S

(2x – 14)°

(6x + 16)°

J

D

U

9y°

(3x + 20)°

x = y =

m� =

m� =

m� =

m� =

m� =

m� =

(4x + 7)°

(6x + 15)°

(7x – 12)°

m� =

m� =

m� =

Statements ReasonsGivenGiven

LHTCEReflexivePOC

SHTCESSTC

500540760

980470350

X IS X IO