Answer:
The correct option is D) SAS
Step-by-step explanation:
Consider the provided statement.
SAS Similarity Theorem: If two sides of a triangle are proportional to the two sides of another triangle and the included angle in both are congruent, then the two triangles are similar.
Statement 1: Let ΔABC be an isosceles triangle where AB = BC.
Reason 1: Given
Statement 2: Create point D on so that bisects ∠ABC as shown.
Reason 2: Constructing an angle bisector.
Statement 3: m∠ABD = m∠DBC
Reason 3: Definition of angle bisector
Statement 4: BD = BD
Reason 4: Reflexive Property of Equality
Statement 5: ΔABD ≅ ΔCBD
Reason 5: SAS
Statement 6: m∠BAC = m∠BCA
Reason 6: Corresponding angles of congruent triangles are equal.
From Reflexive Property of Equality we know BD=BD, m∠ABD = m∠DBC definition of angle bisector and AB = BC, which follows the Side angle side (SAS) similarity.
