Question

name
6-1 reteach to build understanding
kites and trapezoids

1. complete the statements below.

a kite is a quadrilateral with at least one pair of consecutive congruent sides.
the diagonals of a kite are perpendicular.
at least one diagonal of a kite bisects the other.
a trapezoid is a quadrilateral with at least one pair of opposite parallel sides.
the length of a trapezoid’s midsegment is the average of the lengths of the parallel sides.
an isosceles trapezoid is a trapezoid with congruent base angles. the diagonals of an isosceles trapezoid are congruent.
image of kite abcd if \\(\overline{ab} \cong \underline{\quad}\\) and \\(\overline{bc} \cong \underline{\quad}\\), then \\(\overline{bd} \perp \underline{\quad}\\) and \\(\overline{ac}\\) bisects \\(\underline{\quad}\\).
image of trapezoid defg with midsegment xy if \\(\overline{ef} \parallel \underline{\quad}\\), then \\(\underline{\quad} = (ef + dg) \div 2\\).
image of isosceles trapezoid jhlk if \\(\overline{jk} \parallel \underline{\quad}\\) and \\(\underline{\quad} \cong \overline{jh}\\), then \\(\underline{\quad} \cong \angle l\\) and \\(\overline{jl} \cong \underline{\quad}\\).

1. martin claimed that \\(ru = tu\\) because qrst is a kite. what was his error?

image of kite qrst with diagonals qs and rt intersecting at u

1. find qr.

\\(qr = (no + \underline{\quad}) \div \underline{\quad}\\)
\\(qr = (\underline{\quad} + \underline{\quad}) \div 2\\)
\\(qr = 13 \div 2\\)
\\(qr = \underline{\quad}\\)
image of trapezoid nopm with no = 5, mp = 8, and midsegment qr

Explanation:

Step1: Recall midsegment formula

The midsegment of a trapezoid is the average of the two parallel sides. So for trapezoid \(NOPM\) with midsegment \(QR\), the formula is \(QR=\frac{NO + MP}{2}\).

Step2: Identify values

From the diagram, \(NO = 5\) and \(MP = 8\). Substitute into the formula: \(QR=\frac{5 + 8}{2}=\frac{13}{2}=6.5\). Also, filling the blanks: first blank is \(MP\), second is \(2\), then \(5\) and \(8\), and finally \(6.5\) (or \(\frac{13}{2}\)).

Answer:

For the blanks: \(QR=(NO + \boldsymbol{MP})\div\boldsymbol{2}\); \(QR=(\boldsymbol{5}+\boldsymbol{8})\div2\); \(QR = \boldsymbol{6.5}\) (or \(\frac{13}{2}\))