Question

Geometry 1 help!!!

Answer 1

Arrange the reasons for the proof in the correct order.

Prove: If two points are collinear, then the two points lie on the same line.

A. By definition, the two lines are not collinear.
B. If two points do not lie on the same line, then they are not collinear. Therefore, if two points are collinear, then they lie on the same line (proof by contraposition).
C. Assume that the two points lie on different lines.

A.
A, C, B
B.
B, C, A
C.
C, A, B
D.
C, B, A

Answer 2

If a number is not divisible by 3, then it is not divisible by 6.

Answer 3

Analyze the statements below and complete the instructions that follow.

Given: A rhombus is a quadrilateral with 4 congruent sides.
Prove: If quadrilateral ABCD does not have 4 congruent sides, then it is not a rhombus.

Determine the first step to prove this statement using proof by contradiction.

A.
Assume ABCD does not have 4 congruent sides and is a rhombus.
B.
Assume ABCD has 4 congruent sides and is not a rhombus.
C.
Assume ABCD has 4 congruent sides and is a rhombus.
D.
Assume ABCD is not a rhombus.

Answer 4

Given: p is true
Prove: p → q is true
Assume ~q is true. Then ~q → r, and r → s. Since s → ~p, ~q → ~p by the law of syllogism. Therefore, p → q is true.

What type of proof is illustrated above?

A.
proof by contradiction
B.
proof by contraposition
C.
proof by law of detachment
D.
proof by law of syllogism

Answer 5

Given that the statement below is represented by p → q, determine the statement that represents ~q.

If two planes intersect, then their intersection is a line.

A.
Two planes intersect.
B.
Their intersection is not a line.
C.
Two planes do not intersect.
D.
Their intersection is a line.

Answer 6

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