Ch 4 Notesheet Key
Ch 4 Notesheet Key
Ch 4 Notesheet Key
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<strong>Ch</strong> 4 Note Sheet L1 <strong>Key</strong><br />
4.8 Proving Special Triangle Conjectures<br />
Name ___________________________<br />
Equilateral/Equiangular Triangle Conjecture<br />
Every equilateral triangle is equiangular.<br />
Conversely, every equiangular triangle is equilateral.<br />
Vertex Angle Bisector Conjecture<br />
In an isosceles triangle, the bisector of the vertex angle is also the altitude and the median<br />
to the base and the perpendicular bisector of the base.<br />
Isosceles Triangle with vertex angle A, AB = AC.<br />
Median BM<br />
A<br />
Altitude BL<br />
L<br />
Angle Bisector BS<br />
AB = 3.36 in.<br />
AC = 3.36 in.<br />
CB = 4.34 in.<br />
C<br />
M<br />
S<br />
B<br />
Isosceles Triangle with Vertex Angle B<br />
B<br />
A<br />
EMD<br />
C<br />
Median BM<br />
AM = 1.64 in.<br />
MC = 1.64 in.<br />
Altitude BE<br />
m∠AEB = 90°<br />
Angle Bistector BD<br />
m∠ABD = 27°<br />
m∠DBC = 27°<br />
Medians to the Congruent Sides Theorem<br />
In an isosceles triangle, the medians to the congruent sides are congruent.<br />
Angle Bisectors to the Congruent Sides Theorem<br />
In an isosceles triangle, the angle bisectors to the congruent sides are congruent.<br />
Altitudes to the Congruent Sides Theorem<br />
In an isosceles triangle, the altitudes to the congruent sides are congruent.<br />
A<br />
A<br />
A<br />
N<br />
M<br />
S<br />
P<br />
T<br />
L<br />
C<br />
C<br />
C<br />
B<br />
B<br />
B<br />
Medians MC = BN Angle Bisectors PC = BS Altitudes BT = LC<br />
S. Stirling Page 15 of 15
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