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CORRESPONDING
PARTS OF CONGRUENT
TRIANGLES ARE
CONGRUENT

1. Solve corresponding parts of
congruent triangles; and
2. Prove that two triangles are
congruent

Given the ∆𝐴𝐵𝐶 is congruent to ∆𝑃𝑄𝐶,
complete the following statements.
B
A
C
Q
P

I. 𝑨𝑩 = 𝑷𝑸 = ________𝒄𝒎
B
A
C
Q
P

B
A
C
Q
P
6cm
II. 𝐁𝐂 = ________ = ________𝒄𝒎

B
A
C
Q
P
5cm
III. 𝐂𝐏 = ________ = ________𝒄𝒎

B
A
C
Q
P
𝟑𝟎°
𝟏𝟐𝟎°
𝟑𝟎°
IV. ∠𝑪𝑩𝑨 = ________ = ________°

CPCTC(Corresponding parts of
Congruent triangles are
congruent)
Corresponding parts of congruent
triangles, when two triangles are proved to
be congruent, then each part of one
triangle – three sides and three angles, is
congruent to the corresponding parts of the
other triangle

Given: 𝐵𝐶 ≅ 𝐴𝐷, 𝐵𝐶 ∥ 𝐴𝐷
Prove: ∠𝐵 ≅ ∠𝐷
Example 1
A
B C
D

Given: 𝐵𝐶 ≅ 𝐴𝐷, 𝐵𝐶 ∥ 𝐴𝐷
Prove: ∠𝐵 ≅ ∠𝐷
A
B C
D
Statements Reasons
1. 𝐁𝐂 ≅ 𝐀𝐃, 𝐁𝐂 ∥ 𝐀𝐃 1. Given
2. ∠𝐁𝐂𝐀 ≅ ∠𝐃𝐀𝐂 2. Parallel – Alternative Interior
Angle Postulate
3. 𝐀𝐂 ≅ 𝐀𝐂 3. Reflexive Property of
Congruence
4. ∆𝐁𝐂𝐀 ≅ ∆𝐃𝐀𝐂 4. SAS Postulate
5. : ∠𝐁 ≅ ∠𝐃 5. CPCTC

Given: ∠𝐵𝐴𝐷 ≅ ∠𝐶𝐴𝐷,∠𝐵𝐷𝐴 ≅ ∠𝐶𝐷𝐴
Prove: 𝐴𝐵 ≅ 𝐴𝐶
Example 2
A
B D
C

A
B D
C
Given: ∠𝐵𝐴𝐷 ≅ ∠𝐶𝐴𝐷,∠𝐵𝐷𝐴 ≅ ∠𝐶𝐷𝐴
Prove: 𝐴𝐵 ≅ 𝐴𝐶
𝑺𝒕𝒂𝒕𝒆𝒎𝒆𝒏𝒕𝒔 𝑹𝒆𝒂𝒔𝒐𝒏𝒔
1. ∠𝑩𝑨𝑫 ≅ ∠𝑪𝑨𝑫
∠𝑩𝑫𝑨 ≅ ∠𝑪𝑫𝑨
Given
2. 𝑨𝑫 ≅ 𝑨𝑫 Reflexive Property of
Congruence
3. ∆𝑩𝑨𝑫 ≅ ∆𝑪𝑨𝑫 ASA Postulate
4. 𝑨𝑩 ≅ 𝑨𝑪 CPCTC

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CPCTC-lesson-17.1.pptx

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CPCTC-lesson-17.1.pptx