Module 1 Lesson 23 ­ ASA, AAS.notebook

1

October 27, 2016

Oct 26­9:06 AM

Lesson 23 ASA and AAS

#6, 7, 9HW

Do Now:Proof on front page

Quiz Wednesday

Oct 14­8:36 AM

1. Given

2. An angle bisector divides an angle into 2 congruent parts

3. Reflexive Property

4. SAS≅SAS

1. AE bisects <BCD, BC≅DC

2. <BCA≅<ACD

3. AC≅AC

4. ΔABC ≅ ΔADC

Module 1 Lesson 23 ­ ASA, AAS.notebook

2

October 27, 2016

Oct 14­8:35 AM

1. Given1. JM≅KL, JM l ML, LM l ML

2. <JML and <KLM are both right angles

2. Perpendicular lines form right angles

3. <JML≅<KLM 3. All right angles are congruent

4. ML≅ML 4. Reflexive Property

5. ΔJML≅ΔKLM 5. SAS≅SAS

Translation then Reflection

Oct 14­8:35 AM

1. Given1. <1 <2, BC DC

2. Reflexive Property2. AC AC

3. ΔABC ΔADC 3. SAS SAS

Reflection

Module 1 Lesson 23 ­ ASA, AAS.notebook

3

October 27, 2016

Oct 14­8:35 AM

1. Given1. KM and JN bisect each other

2. KL LM, JL LN 2. A bisector divides a segment into two congruent parts

3. <KLJ <NLM 3. Vertical angles are congruent

4. ΔJKL ΔNML 4. SAS SAS

Rotation

Oct 14­8:35 AM

1. Given

3. SAS SAS

1. ΔRST is isosceles with RS RT, SY TZ

2. <RST <RTS 2. In a triangle, angles opposite congruent sides are congruent

3. ΔRSY ΔRTZ

Reflection

Module 1 Lesson 23 ­ ASA, AAS.notebook

4

October 27, 2016

Oct 14­8:37 AM

Oct 14­8:37 AM

1. Given1. M is the midpoint of HP, <H≅<P

2. A midpoint divides a segment into 2 congruent parts2. HM≅MP

3. <HMG ≅ <RMP 3. Vertical angles are congruent

4. ΔGHM≅ΔRPM 4. SAS ≅ SAS

Reflection

Module 1 Lesson 23 ­ ASA, AAS.notebook

5

October 27, 2016

Oct 14­8:37 AM

1. Given1. <J≅<M, JA≅MB, JK≅ML

2. KL ≅ KL 2. Reflexive Property

3. JK + KL ≅ KL + ML 3. Addition Postulate

4. ΔAJL≅ΔBMK 4. SAS ≅ SAS

Oct 14­8:37 AM

2. Linear Pairs form supplementary angles

3. Substitution Property

7. Reflexive Property

5. Perpendicular lines form right angles

6. All right angles are congruent

8. AAS ≅ AAS

2. <1 + <CDB = 180 <2 + <BDA = 180

3. <1 + <CDB = <2 + <BDA

5. <BCD and <BAD are right angles

6. <BCD ≅ <BAD

7. BD ≅ BD

8. ΔBCD≅ΔBAD

4. <CDB ≅ <BDA4. Subtraction Postulate

Module 1 Lesson 23 ­ ASA, AAS.notebook

6

October 27, 2016

Oct 14­8:37 AM

1. <A≅<D, AE≅DE 1. Given

2. <AEB≅<DEC 2. vertical angles are congruent

3. Δ AEB ≅ ΔDEC 3. AAS≅AAS

Reflection

Oct 14­8:38 AM

1. AB l BC, DE l EF 1. Given

2. <B, <E are right angles 2. Perpendicular lines form right angles

3. <B ≅ <E 3. All right angles are congruent

4. <EFC ≅ <BCF 4. If two parallel lines are cut by a transversal then

alternate interior angles are congruent

5. FC ≅ FC 5. Reflexive Property

6. AC ≅ FD 6. Addition Property

7. ΔABC ≅ ΔDEF 7. AAS≅ AAS

Rotation, Translation

BC || EF, EF≅DC

Module 1 Lesson 23 ­ ASA, AAS.notebook

7

October 27, 2016

Oct 14­8:38 AM

AC ≅ CB, D is the midpoint of ABGiven

AD≅ DB A midpoint divides a segment into two congruent parts

<A ≅ <B In a triangle, angles opposite congruent sides are congruent

ΔACD ≅ ΔBCD SAS ≅ SAS

Reflection

Oct 14­8:38 AM

DF

1. Given1. AC and DF bisect each other at E and AD≅CF

2. A bisector divides a segment into two congruent parts2. AE≅EC, DE≅EF

3. SSS≅SSS3. ΔADE≅ΔCFE

Module 1 Lesson 23 ­ ASA, AAS.notebook

8

October 27, 2016

Oct 14­8:38 AM

<B ≅ <D, BD bisects AE Given

AC ≅ CE A bisector divides a segment into two congruent parts

<ACB ≅ <DCE Pairs of vertical angles are congruent

ΔABC ≅ ΔEDC AAS ≅ AAS