4b - 7 - 15b + 3 simplified
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Answer: 1. Angle-Side-Angle (ASA) Postulate
2. Corresponding parts of congruent triangles are congruent (CPCTC)
Step-by-step explanation:
Given : ABC is a triangle,
In which, ∠BAC ≅ ∠BCA
To prove : Δ ABC is an isosceles triangle,
Proof:
Construct a perpendicular bisector from point B to Line segment AC,
Label the point of intersection between this perpendicular bisector and Line segment AC as point D
∠BAC ≅ ∠BCA ( Given )
Since, ∠BDA ≅ ∠BDC ( Right angles )
AD ≅ DC (By the definition of a perpendicular bisector. )
Thus, By ASA postulate of congruence,
Δ BAD ≅ Δ BCD
⇒ AB ≅ BC ( By CPCTC )
⇒ ΔABC is isosceles ( by definition of an isosceles triangle )
