Download 4.6 Using Congruent Triangles

4.6 Using Congruent Triangles
Corresponding parts of congruent
triangles are congruent.
*Special case of definition of congruent figures.
*Used after proving triangles congruent.
CPCTC
Statements
1. <1 ≡ <2
2. <ABC suppl. <1
<DEC suppl <2
3. < ABC ≡ < DEC
4. <ACB ≡ <DCE
5.
6. ACB ≡
DCE
7. .
Reasons
1.
2.
3.
4.
5.
6.
7.
Given
Angles in a linear pair are ≡.
Suppl. Of ≡ <s are ≡.
Vertical <s are ≡ .
Given
AAS ≡
CPCTC
The triangles are congruent
by ASA. CPCTC says that
AB= DE. If you can measure
length of DE, then you will
know the length of AB.
The supplements of < 1 and <2 are congruent. DE is reflexive.
∆ DEB ≡ ∆ DEC by AAS.
DB ≡ DC because of CPCTC.
AD is reflexive. This makes ∆ ABD ≡ ∆ ACD by SAS.
Geometry
• Page 257(1-14, 28, 41-43)
• Page 259 (18-24, 29-31, 33-35, 44-46)