Question

Ms. Chamberlain's students are discussing the following quadrilaterals and their diagonals. Model: Square cut into diagonals, Rhombus cut into 4ths, Kite, split vertically and horizontally. Ms. Chamberlain asks her students what they notice about the diagonals in the quadrilaterals. One student says, "I noticed that the diagonals of the quadrilaterals always cross at a right angle." Of the following sets of quadrilaterals, for which set is the student's conjecture always True?

A. Squares and Rectangles
B. Rhombi and Parallelograms
C. Kites and Trapezoids
D. Squares and Rhombi

Answer 1

The student's conjecture that diagonals of the quadrilaterals always intersect at right angles is correct for Squares and Rhombi only, so the answer is D. Squares and Rhombi.

Step-by-step explanation:

The student's conjecture that the diagonals of the quadrilaterals always cross at a right angle is only true for certain types of quadrilaterals. Specifically, this is true for:

• Squares: Where the diagonals are both equal in length and bisect each other at a right angle.
• Rhombi: Similar to squares, diagonals bisect at right angles, but the lengths may differ.

Therefore, the correct answer is D. Squares and Rhombi. This is not necessarily true for rectangles or parallelograms, as in rectangles the diagonals are equal but do not intersect at a right angle, and in the general case of parallelograms, neither the lengths nor the angles at which the diagonals intersect are constrained to be right angles. Kites have diagonals that intersect at a right angle, but this is not true for trapezoids.