Question

joshua said the following statements are valid.
select all the statements that are invalid.

all quadrilaterals have four sides.
a trapezoid cannot have a right angle.
a triangle is a polygon with three sides.
a polygon with five sides is a pentagon.
all equiangular quadrilaterals are congruent.

Explanation:

Step1: Analyze each statement

• All quadrilaterals have four sides: By definition, a quadrilateral is a polygon with four sides. So this statement is valid.
• A triangle is a polygon with three sides: By definition, a triangle is a polygon with three sides. So this statement is valid.
• A polygon with five sides is a pentagon: By definition, a pentagon is a polygon with five sides. So this statement is valid.
• A trapezoid cannot have a right angle: A right - trapezoid has two right angles. So this statement is invalid.
• All equiangular quadrilaterals are congruent: Equiangular quadrilaterals (like rectangles) can have different side lengths. For example, a rectangle with length \(l = 4\) and width \(w=2\) and a rectangle with \(l = 6\) and \(w = 3\) are equiangular (all angles \(90^{\circ}\)) but not congruent. So this statement is invalid.

Answer:

• Valid statements: "All quadrilaterals have four sides", "A triangle is a polygon with three sides", "A polygon with five sides is a pentagon"
• Invalid statements: "A trapezoid cannot have a right angle", "All equiangular quadrilaterals are congruent"