Question

name:
homework lesson 5.11
directions: now graph and label quadrilateral to prove that it is parallelogram

1. graph and label quadrilateral smrt with vertices s(1, 0), m(6, 7), r(8, 1) and t(3, - 6)

b) prove that quadrilateral smrt is a parallelogram.

Explanation:

Step1: Plot vertices on coordinate plane

Plot points: $S(1, 0)$, $M(6, 7)$, $R(8, 1)$, $T(3, -6)$ and connect them in order to form quadrilateral $SMRT$.

Step2: Calculate slope of SM

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m_{SM}=\frac{7-0}{6-1}=\frac{7}{5}$

Step3: Calculate slope of RT

$m_{RT}=\frac{-6-1}{3-8}=\frac{-7}{-5}=\frac{7}{5}$

Step4: Calculate slope of MR

$m_{MR}=\frac{1-7}{8-6}=\frac{-6}{2}=-3$

Step5: Calculate slope of TS

$m_{TS}=\frac{0-(-6)}{1-3}=\frac{6}{-2}=-3$

Step6: Verify parallel sides

Parallel lines have equal slopes. $m_{SM}=m_{RT}$ so $SM \parallel RT$; $m_{MR}=m_{TS}$ so $MR \parallel TS$. A quadrilateral with both pairs of opposite sides parallel is a parallelogram.

Answer:

1. The graph has vertices $S(1, 0)$, $M(6, 7)$, $R(8, 1)$, $T(3, -6)$ connected in sequence to form quadrilateral $SMRT$.
2. Quadrilateral $SMRT$ is a parallelogram because both pairs of its opposite sides have equal slopes (and are therefore parallel): $SM \parallel RT$ (slope $\frac{7}{5}$) and $MR \parallel TS$ (slope $-3$).