Writing Indirect Proofs
Fill in the following proofs with missing statements and/or reasons.
1.
Prove:
S T A T E M E N T S
R E A S O N S
Answer Given
Answer Assumption leading to a contradiction.
Answer Median of a triangle joins any vertex to the midpoint of the opposite side.
Answer Midpoint of a segment divides the segment into two congruent segments.
Answer Reflexive Property
Answer Perpendicular lines form right angles.
Answer All right angles are congruent.
Answer SAS
Answer CPCTC
Answer Contradiction Steps 1 and 9
2.
Answer segments AE and CD are congruent
Answer The altitude of a triangle is a line segment extending from any vertex of a triangle perpendicular to the line containing the opposite side.
Answer angles AEB, and CDB are right angles
Answer angles AEB and CDB are congruent
Answer Angle B is congruent to angle B
Answer AAS
Answer Triangle ABC is isosceles.
Answer An isosceles triangle has two congruent sides.
3.
Answer Assume that segment AB is congruent to segment AC.
Answer Segment BD is congruent to segment DC.
Answer Segment AD is congruent to itself.
Answer Triangle ADB is congruent to triangle ADC.
Answer Angle BAD is congruent to angle DAC.
Answer AD bisects angle CAB.
Answer Segment AB is not congruent to segment AC.
4.
Assume Assume that angle 1 and angle 2 are equal.
Answer If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
Answer Angle 1 is congruent to angle 3.
Answer If two angles of a triangle are congruent, the sides opposite them are congruent.
Answer Contradiction steps 5 and 1
Roberts
where
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