Current location - Training Enrollment Network - Mathematics courses - Examples and answers of solving problems by reverse method in junior high school mathematics
Examples and answers of solving problems by reverse method in junior high school mathematics
Example: disproof proves that no two angles in a triangle are right angles.

Known: triangle ABC verification: Angle A, Angle B and Angle C cannot be two right angles.

Analysis: According to the steps of proving the proposition to absurdity, we must first assume that the conclusion that "no two angles in Angle A, Angle B and Angle C are right angles" is invalid, that is, its opposite "two angles in Angle A, Angle B and Angle C are right angles" holds, and then, from this assumption, find out the contradiction.

Proof: Suppose that two of Angle A, Angle B and Angle C are right angles, and let Angle A= Angle B=90 degrees.

Then angle A+ angle B+ angle C=90 degrees +90 degrees+angle C is greater than 180 degrees, which contradicts the theorem of triangle interior angle sum.

Therefore, angle A= angle B=90 degrees is not valid.

So no two right angles in a triangle can be right angles.