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4-7 & 10-3 Proofs: Medians Altitudes Angle Bisectors Perpendicular Bisectors
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Statements Reasons . is an altitude D is midpoint of is a median Given
Definition of altitude Reflexive Property ASA CPCTC Definition of a midpoint Definition of a median C D E F Given: Prove: is a median is an altitude
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Prove that the altitude of an isosceles triangle
Statements Reasons ΔABC is isosceles is an altitude Given Definition of isosceles Δ ITT Definition of Altitude AAS CPCTC Definition of bisector A D C B Prove that the altitude of an isosceles triangle drawn from the vertex is also an angle bisector.
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Statements Reasons . A is the midpoint Given Definition of bisector
1 2 . A is the midpoint Given Definition of bisector Definition of midpoint Reflexive property SAS CPCTC Definition of altitude Given: Prove: is the perpendicular bisector of & are altitudes
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Statements Reasons . Definition of lines AAS CPCTC Given: Prove:
B C D E F 1 2 . Definition of lines AAS CPCTC Given: Prove: is the perpendicular bisector of & are altitudes
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Statements Reasons ΔABC is equilateral is a median Given
Definition of equilateral Δ Definition of median Definition of midpoint Reflexive property SSS CPCTC B Prove in an equilateral triangle any median creates two congruent right triangles. C A D
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Statements Reasons . . Prove in an equilateral triangle any median
B C A D Prove in an equilateral triangle any median creates two congruent right triangles.
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