Download Honors Geometry Section 4.3 cont. Using CPCTC

Honors Geometry Section 4.3 cont.
Using CPCTC
In order to use one of the 5
congruence postulates / theorems
( SSS, SAS, ASA, AAS, RHL )we need
to show that 3 parts of one triangle
are congruent to 3 parts of a
second triangle.
But once we have the two triangles
congruent, we can then state that any of
the other 3 pairs of corresponding angles
or sides are congruent by CPCTC which
stands for
corresponding parts of congruent triangles
are congruent
Note that this statement is just the
definition of congruent triangles.
Let’s prove a couple of things from
Unit IV.
The Isosceles Triangle Theorem
Given: AB = AC
Prove: B  C
D
1) AB = AC
1) Given
2) Draw AD, the altitude from A 2) Every triangle has 3 altitudes
3) AD  BC
3) Def. of altitude
4) ADB & ADC are Rt. Angles 4) Def. of perp.
5) ADB  ADC
5) RAT
6) AD  AD
6) Reflexive Prop.
7) ADB & ADCareRt.Tri. 7) Def. of Rt. Tri.
) ADB  ADC
) B  C
8) RHL
) CPCTC
In an isosceles triangle, the median from the vertex angle bisects the angle.
Given: AB  AC , AD is a median
Prove: AD bisects BAC
1) ---------------------------------------------- 1) Given
2) D is the midpoint of BC
3) BD  DC
2) Def. of median
3) Def. of midpoint
4) AD  AD
4) Reflexive
)BAD  CAD
)BAD  CAD
)CPCTC
) AD bisects BAC
) Def. of Bisects
) SSS
D