Question

HELP PLZ!!! I'M GIVING 15 POINTS FOR IT!!!!!!

Decide whether each statement is true or false. If a statement is true, say which of Euclid’s five postulates apply to it, then write the converse and contrapositive statements, and then decide which of these statements are true (it may help to rewrite the statements in “if-then” form). If it is false, give a counterexample or explain why.


a. A triangle can be drawn from any three points that are not on the same line.

b. A square can be drawn from any four points not on the same line.

c. When two lines intersect, the four angles they make add to 360 degrees.

d. There is only one parallel line to any given line.

Answer 1

a: True "A straight line segment may be drawn from any given point to any other." ( converse, from any given point, a straight line segment may be drawn {true} ) ( contrapositive: from no point, a straight line segment cant be drawn {true})

b: False A trapezoid or rectangle can be formed, which are not necessarily squares

c: True According to postulate 1 "A line can be drawn through any 2 points", and a line must equal 180 degrees, therefore two lines must equal a total of 360 degrees. (converse: from any two points, a line can be drawn {true}") (contrapositive: From no points, a line can not be drawn {true})

d. False The image provided below proves that more than one line is parallel, The postulate used is "A segment can be extended indefinitely to form a straight line" because they are indefinite and will never touch, they are parallel (converse: a straight line can be stretched indefinitely to form a segment. {false}) (contrapositive: a straight line can not be stretched indefinitely to not form a segment. {false})

Answer 2

a. True

b. False

c. True

d. False

Explanation:

a. True

Where, there are three straight lines intersecting one another, and whereby the sum of the interior angles formed between one of the straight lines and the other two is less than 180°, then the other two straight lines will cross if extended further on the same side of the figure where the sum of the intersecting angles between the lines was found to be less than 180°.

The converse statements is that

If three lines are drawn with two of the lines converging, then the third line can be drawn such that the sum of the interior angles between it and the other two lines is less than 180°

The contrapositive statements is that

If the sum of the interior angles between a first line and the other two lines is equal to 180° then the other two lines will not meet

b. False.

The answer is false is false because,

The length of the sides of the square must be equal

The interior angles of the square must also be equal

c. True

From Postulate 1, the sum of two adjacent angles on one side of the two intersecting lines is equal to 180°. So also on the other side of the intersection, the sum of the adjacent angles is equal to 180.

Therefore, we have

180° + 180° = 360°

The converse statements is that

If two lines meet at a point then the sum of angles at the point is 360°

The contrapositive statements is that

If the two lines do not meet, then the sum of angles on each line is 180°

d. False

A parallel line can be drawn from any point not on the line.