Math 2201 Name: In-class assignment section 2.4-2.6 1. For the regular heptagon shown below, determine the internal angle sum and then find the measure of the indicated angle. 2. Indicate which congruence theorem is being illustrated by each pair of triangles.

(SSS, ASA, SAS, or AAS)

©1 02h0w1b26 8Kduftrak jSXo0fMthwUairseU kLXL0Cs.H B QAVl7la grNiig1hqtws5 kr5efsteorsvHeQdN.A l nMEaPdQeG lwdirtihN LIynzftiSnXirtAen OGyeHofm8eqt9rQy0.X Worksheet by Kuta Software LLC

Kuta Software - Infinite Geometry Name___________________________________

Period____Date________________ASA and AAS Congruence

State if the two triangles are congruent. If they are, state how you know.

1) 2)

3) 4)

5) 6)

7) 8)

9) 10)

-1-

©f M2x0F1S1l YK0uMtwav oSPopfYtpwNaSruez qLULSC7.5 p jA5ljls ordi2gDhctisS trseMsqeVrBvCeFdw.c f IMMandSeQ Gw8i3tShv uIonjf2iRnqiZtmeY vGMeLogmQeCtZrPyl.X Worksheet by Kuta Software LLC

Kuta Software - Infinite Geometry Name___________________________________

Period____Date________________SSS and SAS Congruence

State if the two triangles are congruent. If they are, state how you know.

1) 2)

3) 4)

5) 6)

7) 8)

9) 10)

-1-

BC EF givenC F given

AC DF given

So ABC DEF by SAS.

3. For this pair of congruent triangles, state the corresponding angles and sides. Then give the appropriate congruence theorem and write the congruence statement.

4. Explain why these triangles may not be congruent.

5. What additional piece of information is needed to show that the following pairs of triangles are congruent. By ASA By AAS

4.4 Proving Triangles are Congruent: ASA and AAS 223

1. Name the four methods you have learned for proving triangles congruent.Only one of these is called a theorem. Why is it called a theorem?

Is it possible to prove that the triangles are congruent? If so, state thepostulate or theorem you would use. Explain your reasoning.

2. ¤RST and ¤TQR 3. ¤JKL and ¤NML 4. ¤DFE and ¤JGH

State the third congruence that must be given to prove that ¤ABC £ ¤DEFusing the indicated postulate or theorem.

5. ASA Congruence Postulate 6. AAS Congruence Theorem

7. RELAY RACE A course for a relay race is marked on the gymnasium floor. Your team starts at A, goes to B, then C, then returns to A. The other team starts at C, goes to D, then A, then returns to C. Given that ADÆ ! BCÆ and ™B and ™D are right angles, explain how you know the two courses are the same length.

LOGICAL REASONING Is it possible to prove that the triangles arecongruent? If so, state the postulate or theorem you would use. Explainyour reasoning.

8. 9. 10.

11. 12. 13.W

Y

Z

XK

L

J

M

q

N

E

F

G

H

J

A

B

C Dq

P

S

TR

M

U

R S

T

V

PRACTICE AND APPLICATIONS

A B

C E D

F

A B

C

D E

F

JH

F

D

E GM

N

K

L

J

R T

q

S

GUIDED PRACTICE

A

B C

D

STUDENT HELP

HOMEWORK HELPExample 1: Exs. 8–13Example 2: Exs. 14–22Example 3: Exs. 23–25, 28

Extra Practiceto help you masterskills is on pp. 809and 810.

STUDENT HELP

Vocabulary Check ✓

Concept Check ✓

Skill Check ✓

4.4 Proving Triangles are Congruent: ASA and AAS 223

1. Name the four methods you have learned for proving triangles congruent.Only one of these is called a theorem. Why is it called a theorem?

Is it possible to prove that the triangles are congruent? If so, state thepostulate or theorem you would use. Explain your reasoning.

2. ¤RST and ¤TQR 3. ¤JKL and ¤NML 4. ¤DFE and ¤JGH

State the third congruence that must be given to prove that ¤ABC £ ¤DEFusing the indicated postulate or theorem.

5. ASA Congruence Postulate 6. AAS Congruence Theorem

7. RELAY RACE A course for a relay race is marked on the gymnasium floor. Your team starts at A, goes to B, then C, then returns to A. The other team starts at C, goes to D, then A, then returns to C. Given that ADÆ ! BCÆ and ™B and ™D are right angles, explain how you know the two courses are the same length.

LOGICAL REASONING Is it possible to prove that the triangles arecongruent? If so, state the postulate or theorem you would use. Explainyour reasoning.

8. 9. 10.

11. 12. 13.W

Y

Z

XK

L

J

M

q

N

E

F

G

H

J

A

B

C Dq

P

S

TR

M

U

R S

T

V

PRACTICE AND APPLICATIONS

A B

C E D

F

A B

C

D E

F

JH

F

D

E GM

N

K

L

J

R T

q

S

GUIDED PRACTICE

A

B C

D

STUDENT HELP

HOMEWORK HELPExample 1: Exs. 8–13Example 2: Exs. 14–22Example 3: Exs. 23–25, 28

Extra Practiceto help you masterskills is on pp. 809and 810.

STUDENT HELP

Vocabulary Check ✓

Concept Check ✓

Skill Check ✓

6. For the figures below, find the indicated angle.

Triangle Sum Theorem24°+88°+x=180° 112°+x=180° -112° -112° x=68°

m 1+m 2=m 3 29°+x=87° -29° -29° x=______

©s m2a0q1m1S MKWuGtfad 6SmozfotkwEaWrDe1 GLbLfCl.I h yAKlklM kr4ingCh7tes7 BrqeVsIe9rXv4e7dC.r S pMPaadJed WwAiXtjhN GIsndfGiznFiXtoeq 8GlemoymfeUtgr1yh.c Worksheet by Kuta Software LLC

9)

40°20°

39° ?

10)

60°

65°

35°

?

50°

11) 86°

?

36°

84°

12)

23°35°

27° ?

13)

85°

115°

155°

?

14)

35°20°

156° ?

15)

60°

45°

100°

?

68°

16)

75°

45°

68°

?

79°

-2-

©s m2a0q1m1S MKWuGtfad 6SmozfotkwEaWrDe1 GLbLfCl.I h yAKlklM kr4ingCh7tes7 BrqeVsIe9rXv4e7dC.r S pMPaadJed WwAiXtjhN GIsndfGiznFiXtoeq 8GlemoymfeUtgr1yh.c Worksheet by Kuta Software LLC

9)

40°20°

39° ?

10)

60°

65°

35°

?

50°

11) 86°

?

36°

84°

12)

23°35°

27° ?

13)

85°

115°

155°

?

14)

35°20°

156° ?

15)

60°

45°

100°

?

68°

16)

75°

45°

68°

?

79°

-2-

©s m2a0q1m1S MKWuGtfad 6SmozfotkwEaWrDe1 GLbLfCl.I h yAKlklM kr4ingCh7tes7 BrqeVsIe9rXv4e7dC.r S pMPaadJed WwAiXtjhN GIsndfGiznFiXtoeq 8GlemoymfeUtgr1yh.c Worksheet by Kuta Software LLC

9)

40°20°

39° ?

10)

60°

65°

35°

?

50°

11) 86°

?

36°

84°

12)

23°35°

27° ?

13)

85°

115°

155°

?

14)

35°20°

156° ?

15)

60°

45°

100°

?

68°

16)

75°

45°

68°

?

79°

-2-

7. Create a two-column proof to show that the pair of triangles below are congruent.

Statement Reason

8. Complete the following proof.

Urban School / Math 2B Proof, p. 3

Two Formats for Proof

1. This is an example of a proof in paragraph form. This is the form mathematicians use. Examine

the given information and mark the diagram appropriately. Then fill in the blanks in the proof.

Given: RQ=SQ and RP=SP.

Prove: ∠ R = ∠ S.

The given information is: and

. PQ=PQ because . So

∆PRQ! ∆PSQ because of the

property for congruent triangles. Therefore,

because corresponding parts of congruent

triangles are congruent.

2. This is an example of a proof in two-column form. Some teachers and students prefer this form.

Examine the given information and mark the diagram appropriately. Then fill in the blanks in the

proof.

Given: AC=BC and ∠ 1 = ∠ 2.

Prove: ∠ A = ∠ B.

Proof:

Statements Reasons

1. AC = BC 1.

2. 2. Given

3. CD = CD 3.

4. 4. by SAS property

5. ∠A = ∠ B 5.

R

P

S

Q

1 2

C

A BD

9. Explain why this proof fails to show that the two triangles are congruent.

Geometry End-of-Course Make-up Review 2011 Draft

8

Sample Questions

1. Show that the conjecture is false by finding a counterexample.

If , then .

A. ,

B. ,

C. ,

D. ,

2. Identify errors in reasoning in the following proof: ∠𝐴𝐵𝐶 ≅ ∠𝑃𝑅𝑄

𝐴𝐵 ≅ 𝑃𝑄  

𝐵𝐶 ≅ 𝑄𝑅

Given

Δ𝐴𝐵𝐶 ≅ Δ𝑃𝑄𝑅 SAS

A. The student mixed up the sides and should have said  𝐴𝐶 ≅ 𝑃𝑅 instead of saying 𝐴𝐵 ≅ 𝑃𝑄 in order to conclude Δ𝐴𝐵𝐶 ≅ Δ𝑃𝑄𝑅 by SAS.

B. The student mixed up the angles and should have said ∠𝐴𝐵𝐶 ≅ ∠𝑃𝑄𝑅,   instead of saying ∠𝐴𝐵𝐶 ≅ ∠𝑃𝑅𝑄 in order to conclude Δ𝐴𝐵𝐶 ≅ Δ𝑃𝑄𝑅 by SAS.

C. The student needed to know that 𝐴𝐵 ≅ 𝑃𝑅 in order to conclude  Δ𝐴𝐵𝐶 ≅ Δ𝑃𝑄𝑅 by SAS. D. The student mixed up which triangles were congruent. Using the given information, ∠𝐴𝐵𝐶 ≅

∠𝑃𝑅𝑄, 𝐴𝐵 ≅ 𝑃𝑄, 𝑎𝑛𝑑  𝐵𝐶 ≅ 𝑄𝑅 the student should have concluded Δ𝐴𝐵𝐶 ≅ Δ𝑃𝑅𝑄.