4 years ago

If ABCD is a parallelogram, then which statement is true?

Mathematics

1 answer:

hjlf4 years ago

7 0

B. Segment AB is congruent to segment CD.

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Step-by-step explanation:

It is the pythagorean Theorem and there is this special rule my teacher always told me to follow that means it is always 3, 4, and 5. Trust me, I had this problem before. It is 5cm just use the pythagorean theorem.

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If $u$ and $v$ are supplementary angles, then

$u+v=180^{\circ}~~~~~\mathbf{(i)}$

The ratio of $u$ and $v$ is $\dfrac{7}{13}:$ 

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Substitute $\mathbf{(ii)}$ into $\mathbf{(i)}:$

$\dfrac{7v}{13}+v=180^{\circ}\\\\\\ \left(\dfrac{7}{13}+1 \right )\cdot v=180^{\circ}\\\\\\ \left(\dfrac{7}{13}+\dfrac{13}{13} \right )\cdot v=180^{\circ}\\\\\\ \dfrac{20}{13}\cdot v=180^{\circ}\\\\\\ v=180^{\circ}\cdot \dfrac{13}{20}\\\\\\ \boxed{\begin{array}{c} v=117^{\circ} \end{array}}$

From $\mathbf{(i)},$ we find the measure of $u:$

$u=180^{\circ}-v\\\\ u=180^{\circ}-117^{\circ}\\\\ \boxed{\begin{array}{c} u=63^{\circ} \end{array}}$

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