The document discusses the concept of CPCTC (Corresponding Parts of Congruent Triangles are Congruent). It states that once two triangles are proven to be congruent using one of the five congruence criteria (SSS, SAS, ASA, AAS, HL), then all corresponding sides and angles of the triangles are also congruent due to CPCTC. The document provides examples of using CPCTC to prove specific angles or sides of triangles are congruent after first showing the overall triangles are congruent.
Determine what additional information is needed to prove two triangles congruent by a given theorem.
Create two-column proofs to show that two triangles are congruent.
Determine what additional information is needed to prove two triangles congruent by a given theorem.
Create two-column proofs to show that two triangles are congruent.
Parallelogram is a quadrilateral with two pairs of parallel sides.
There are 6 properties of parallelogram.
1. A diagonal of a parallelogram divides it into two congruent triangles.
2. Opposites sides of a parallelogram are congruent.
3. Opposite angles of a parallelogram are congruent.
4. Consecutive angles of a parallelogram are supplementary.
5. If one angle in a parallelogram is right, then all angles are right.
6. The diagonals of a parallelogram bisect each other.
Parallelogram is a quadrilateral with two pairs of parallel sides.
There are 6 properties of parallelogram.
1. A diagonal of a parallelogram divides it into two congruent triangles.
2. Opposites sides of a parallelogram are congruent.
3. Opposite angles of a parallelogram are congruent.
4. Consecutive angles of a parallelogram are supplementary.
5. If one angle in a parallelogram is right, then all angles are right.
6. The diagonals of a parallelogram bisect each other.
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1. CPCTC
The student will be able to (I can):
• Show that corresponding parts of congruent triangles are
congruent.
• Use CPCTC to solve problems
2. CPCTCCPCTCCPCTCCPCTC – an abbreviation for “Corresponding Parts of
Congruent Triangles are Congruent.”
Once we know two triangles are congruent, we then know
that all of their corresponding sides and angles are
congruent.
To use CPCTC, first prove the triangles congruent using SSS,
SAS, ASA, AAS, or HL, and then use CPCTC to state that the
other parts of the triangle are also congruent.
3. Example Given: ∠LBG ≅ ∠OGB
Prove: ∠L ≅ ∠O
1. 1. Given
2. ∠LBG ≅ ∠OGB 2. Given
3. 3. Reflex. prop. ≅
4. ΔLBG ≅ ΔOGB 4. SAS
5. ∠L ≅ ∠O 5. CPCTC
L
B
O
G
,BL GO≅
BL GO≅
BG GB≅
4. Example Given:
Prove: ∠O ≅ ∠R
To prove the angles congruent, we can
break this shape into two triangles, prove
the triangles congruent, and then use
CPCTC to prove the angles congruent.
R
U
O
F
,FO FR UO UR≅ ≅
5. Example: Given:
Prove: ∠O ≅ ∠R
R
U
O
F
StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons
1. 1. Given
2. 2. Given
3. 3. Refl. prop. ≅
4. ΔFOU ≅ ΔFRU 4. SSS
5. ∠O ≅ ∠R 5. CPCTC
FO FR≅
UO UR≅
UF UF≅
,FO FR UO UR≅ ≅