Problem: rewrite each statement (in ordinary english, not symbols), making the q

Question

Problem: rewrite each statement (in ordinary english, not symbols), making the quantifiers explicit; then negate the quantifed statement.

Statement a.) if L is a line and A is a point not on hat line, then there are no lines that contain A and are parallel to L.

statement b.) If ABC and DEF are triangles such that AB is congruent to DE, AC is congruent to DF, and BC is congruent to EF, then angle A is congruent to angle D, angle B is congruent to angle E and angle C is congruent to angle F.

Statement c.) if x^2, then x is not a rational number.

Thank You!

Explanation / Answer

Statement (a)

For any number of line in order to be parallel. The distance between them shoudl be equal at any point.

If we draw any line passing from point A contained in L. Then at point A distance between them is 0 and any other point other than A, distance is >0.

So, we conclude that if L is a line and A is a point not on hat line, then there are no lines that contain A and are parallel to L.

Statement B:

IF SSS hold then triangle is conruent.

We know that:

If two triangles are congruent, then each part of the triangle (side or angle) is congruent to the corresponding part in the other triangle. This is the true value of the concept; once you have proved two triangles are congruent, you can find the angles or sides of one of them from the other.

In sort:

"Corresponding Parts of Congruent Triangles are Congruent".

Hence:

then angle A is congruent to angle D, angle B is congruent to angle E and angle C is congruent to angle F.

Statement C:

Suestion is not clear.

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