20. Given: ?ABC is isos. with AB ? AC. D is midpt. of AB. E is midpt. of AC. Prove: ?PBC is isos. Statement | Reason Triangle ABC is isosceles with Segment AB congruent to segment AC | given D is the midpoint of segment AB | given E is the midpoint of Segment AC | given ?ABC is congruent to ?ACB | if ? then ? ?PBC ? ?PCB | angle subtraction PB ? PC | if ? then ? BC ? BC | reflexive property Triangle PBC is isosceles | Definition of isosceles
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Given: Triangle ABC is isosceles with AB = AC. D is the midpoint of AB and E is the midpoint of AC. Prove: Triangle PBC is isosceles. Statement 1: Triangle ABC is isosceles with AB congruent to AC. Reason: Given Statement 2: D is the midpoint of AB. Reason: Given Statement 3: E is the midpoint of AC. Reason: Given Statement 4: Angle ABC is congruent to angle ACB. Reason: if isosceles then angles congruent Statement 5: Angle PBC is congruent to angle PCB. Reason: angle subtraction Statement 6: BC is congruent to BC. Reason: Reflexive property Statement 7: Triangle PBC is isosceles. Reason: Definition of isosceles
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