Triangle CongruenceCPCTC

SWBAT: Use CPCTC to prove parts of triangles are congruent.

SWBAT: Use CPCTC to prove parts of triangles are congruent.

SWBAT: Use CPCTC to prove parts of triangles are congruent.

SWBAT: Use CPCTC to prove parts of triangles are congruent.

Given

S Midpoint 2 segments

⊥ right angles

A 𝒂𝒍𝒍 right angles are

𝑨𝑪 𝑨𝑪SSAS (2, 4, 5)

∡BAC ∡DAC CPCTC

Z

SWBAT: Use CPCTC to prove parts of triangles are congruent.

ReasonsStatements

5. SSS (2, 3, 4)5. ∆XYW ∆ZYW

4. Reflex. Prop.

2. Midpoint 2 segments

1. Given

2. XW ZW

4. YW YW

3. Given

1. W is the mdpt of XZ

3. XY YZ

(S)

(S)

(S)

6. ∡XYW ∡ZYW 6. CPCTC

X

XYW ZYW By SSS

Prove: PQ PS

Given: PR bisects QPS and QRS.

SWBAT: Use CPCTC to prove parts of triangles are congruent.

ReasonsStatements

1. Given

4. ∆PQR ∆PSR 4. ASA (2, 3, 2)

(A)

(S)

(A)

1. PR bisects QPS and QRS

3. Reflexive Prop.3. PR PR

2. ∡1 ∡2

∡3 ∡4

2. Angle bis. 2 ∡𝑠

X

5. PQ PS 5. CPCTC

12

34PQR PSR

By ASA

ReasonsStatements

7. 7. Given

(A)

1. Given

5. FC FC

6. Addition Post. (4, 5)

2. lines right ∡s

1.

3. All right ∡s

4. Given

2. ∡1 and ∡2 are right s

3. ∡1 ∡2

5. Reflexive Prop.

8. ∆EDF ∆ BAC 8. AAS (3,7,6)

(S)

SWBAT: Use CPCTC to prove parts of triangles are congruent.

1

2

4.

6. DF AC

9. 9. CPCTC

(A)

SWBAT: Use CPCTC to prove parts of triangles are congruent.

SWBAT: Use CPCTC to prove parts of triangles are congruent.

ReasonsStatements

1. 1. Given2. ∡C ∡C 2. Reflexive Property3. ∡ADB suppl. ∡BDC

∡BEA suppl. ∡AEC

3. Linear Pair Thm

4. ∡BDC ∡AEC 4. Congruent Suppl. Thm

SA

A

5. BDC AEC 5. AAS (2, 4, 1)6. 6. CPCTC

SWBAT: Use CPCTC to prove parts of triangles are congruent.

SWBAT: Use CPCTC to prove parts of triangles are congruent.

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