Question

1. consider these two statements:

p: a triangle is a square
q: a rectangle is a quadrilateral.
select all of the true statements.
a ~p
b ~q
c p ∧ q
d p ∨ q
e ~p ∧ q
f p ∨ ~q

1. statements 1 and 2 are true conditional statements.

statement 1: if a figure is a square, then it is a rectangle.
statement 2: if a figure is a rectangle, then it is a parallelogram.
which conclusion is valid?
a if figure a is a square, then figure a is a parallelogram.
b if figure a is not a square, then figure a is not a parallelogram.
c if figure a is a parallelogram, then figure a is a square.
d if figure a is a rectangle, then figure a is a square.

1. complete each postulate.

if two a lines b planes intersect, then their intersection is a point.
through three noncollinear points there is exactly one a line b plane .

1. given: \\( \overline { a b } \cong \overline { c d } \\)

prove: \\( \overline { a c } \cong \overline { b d } \\)
complete the proof.

Explanation:

Step1: Analyze statement 5

• For statement 3: \(AB + BC=BC + CD\), since we are adding \(BC\) to both sides of \(AB = CD\), this is based on the Addition Property of Equality.
• For statement 4: \(AB + BC = AC\) and \(BC + CD=BD\) is based on the Segment Addition Postulate which states that if \(B\) is between \(A\) and \(C\), then \(AB + BC=AC\) and if \(C\) is between \(B\) and \(D\), then \(BC + CD = BD\)

Answer:

1. A, 4. B