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Given: ΔABC is an isosceles triangle where AB = BC.

Prove: m∠BAC = m∠BCA




Proof:
Statement Reason
1. Let ΔABC be an isosceles triangle where AB = BC. given
2. Create point D on so that bisects ∠ABC as shown. constructing an angle bisector
3. m∠ABD = m∠DBC definition of angle bisector
4. BD = BD
5. ΔABD ≅ ΔCBD SAS
6. m∠BAC = m∠BCA Corresponding angles of congruent triangles are equal.
20
What is the reason for statement 4 in this proof?
A.
Transitive Property of Equality
B.
definition of midpoint
C.
definition of parallel lines
D.
Reflexive Property of Equality
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Given: ΔABC is an isosceles triangle where AB = BC. Prove: m∠BAC = m∠BCA Proof: Statement-example-1
User Scradam
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4.0k points

2 Answers

9 votes

You are comparing side AB, angle ABD, and side BD in one triangle to side CB, angle CBD, and side BD in the other triangle. That is, you are comparing a Side, Angle, and Side in each triangle. The SAS postulate is the reason the triangles are congruent.

User Marek Lewandowski
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4.7k points
6 votes

Answer:

Transitive Property of Equality

Explanation:

User Winson
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3.9k points