Download Geometry Notes G.6 Isosceles, Equilateral Triangles Mrs. Grieser

Geometry Notes G.6 Isosceles, Equilateral Triangles
Mrs. Grieser
Name: _____________________________________________ Date: ______________ Block: ________
Isosceles and Equilateral Triangles
Base Angles Theorem
If two sides of a triangle are congruent, then the angles
opposite them are congruent.
Converse of Base Angles Theorem
If two angles of a triangle are congruent, the sides opposite
them are congruent.
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.
Examples
a) Given RT  ST .
Name two
congruent angles.
b) Find AB and AC in
the triangle at right.
c) In the diagram find:
1) WY
2) mWXY
d) mDEF  90 .
Find values of x
and y.
e)
1) What  post. can
be used to prove
that ABC   AED ?
f) Find the values of x and y.
2) Explain why ACD is equiangular.
3) Show that ABD  AEC .
Each angle in
an
equiangular
triangle
measures
_______
Geometry Notes G.6 Isosceles, Equilateral Triangles
g) Find the values of x and y.
h) Given: BD bisects ADC ; DB  AC
Prove: ADC is isosceles
Statements
Reasons
1)________________
1) Given
2) _______________
2) Definition of < bisector
3) 3  4
3) ____________________
4) DB  DB
4) ____________________
5) ______________
5) ASA
6) ______________
6) CPCTC
7) ADC is isosceles
7) _____________________
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