Download Proof Options: Isosceles Triangles

Proof Options: The base angles of an isosceles triangle are congruent.
A
B
C
D
Basic Paragraph Proof:
Since the largest side of a triangle is across from the largest angle, the smallest side is across from the
smallest side, it seem reasonable that if two sides were of equal length the angles across from them, which
are the base angles of an isosceles triangle, would also be equal in measure.
Alternate Paragraph Proof:
If you drop an altitude to the base of the non-congruent side, it is a line of symmetry. It creates two,
symmetric, congruent triangles that have corresponding angles at ends of the non-congruent sides. These
angles, which are the base angles of the isosceles triangle, are congruent as corresponding parts of
congruent triangles.
Two-Column Proof:
Given AB @ AC . Prove
Statements
1. AB @ AC
2. AD bisects ÐBAC
3. ÐABC @ ÐACB
4. AD @ AD
5. DABD @ DACD
6. ÐABD @ ÐACD
ÐABD @ ÐACD
Reasons
1. Given
2. Construction of the Angle Bisector
3. Definition of Angle Bisector
4. Reflexive Property
5. SAS congruence
6. Corresponding Parts of Congruent Triangles are Congruent
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Proof Blocks:
AB @ AC
Construction of the
Angle Bisector
(Blank Block)
AD bisects ÐBAC
ÐABC @ ÐACB
AD @ AD
DABD @ DACD
ÐABD @ ÐACD