1. trapezoid klmn has vertices k(1, 3) , l(3, 1) , m(3, 0) , and n(1, −2) .
is this trapezoid an isosceles trapezoid?
2. in kite wxyz, m∠xwy=47° and m∠zyw=18°.
what is m∠wzy?
enter your answer in the box.
3. what is the length of the midsegment of this trapezoid?
enter your answer in the box.
in kite pqrs, ts=6 cm and tp=8 cm.
what is sp ?
enter your answer in the box.

Step-by-step explanation:

(A) The vertices of the trapezoid KLMN are K(1, 3) , L(3, 1) , M(3, 0) , and N(1, −2)

Now, KL= =\sqrt{8}[/tex]

LM=

MN=

NK=

Now, as KL and MN  are equal, therefore, KLMN is an isosceles trapezoid.

(B) Since  m∠XWY=47°, therefore ∠XWZ=47+47=94° and ∠ZYW=18°, therefore ∠XYZ=36°( as diagonals bisect the angles)

In ΔXWO,

∠XWO+∠WXO+∠WOX=180°(Angle sum property)

∠WXO=43°

Also, from ΔXOY,

∠OXY=72° using the angle sum property.

Therefore, ∠WXY=43+72=115°

Now, sum of all the angles of a quadrilateral is equal to 360°, therefore

∠WXY+∠XYZ+∠YZW+∠ZWX=360°

115°+36°+∠YZW+94°=360°

∠YZW=115°

Therefore,∠WZY=115°

(C) Since, AB and CD are the two parallel lines as the slope of both the sides are equal.

LetM be the mid point of AB, therefore M=

=

Also, let N be the mid point of DC, therefore,

N=

=

Now, length of the mid segment MN=

(D)Given: Kite PQRS,  TS=6cm and TP=8cm

Then, From triangle TSP, we have

the answer is 11.2 (i know i’m late)