Transcript Warm Up - bbmsnclark

Warm-up
SSS
AAS
Not possible
HL
Not possible
SAS
4.6 Isosceles, Equilateral, and
Right Triangles
Students will use the Isosceles
Base Angles Theorem and the HL
theorem to prove triangles
congruent.
A
Given:
ABC, AB  AC, D is the
midpoint of CB.
Prove: B  C
C
D
B
Base Angles Theorem
• If two sides of a triangle are congruent,
then the angles opposite them are
congruent.
• If
AB  ,AC
then
A
B  C.

B
C
Converse of the Base
Angles Theorem
• If two angles of a triangle are congruent,
then the sides opposite them are
congruent.
• If B  C, then

AB .AC
Corollary to the Base Angles Theorem
• If a triangle is equilateral, then it is
equiangular.
Corollary to the Converse of the Base
Angles Theorem
• If a triangle is equiangular, then it is
equilateral.

Hypotenuse-Leg (HL)
Congruence Theorem
• If the hypotenuse and a leg of a right triangle are
congruent to the hypotenuse and a leg of a second
right triangle, then the two triangles are congruent.
• If
, then ABC  DEF.
BC  EF and AC  DF
A
B
D

C
E
F
Example Proof:
• The television antenna is  to the plane
containing the points B, C, D, and E. Each of
the stays running from the top of the antenna
to B, C, and D uses the same length of cable.
Prove that AEB, AEC, and AED are
congruent.
• Given: AEEB,
AEEC, AEED, AB  AC  AD
• Prove:
AEB  AEC  AED

Cool Down