Mathematics: Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ? Since segment XZ is perpendicular to segment WY, angles WZX and XZY are both right angles and congruent. The proportion ________ shows the corresponding sides are proportional, so the triangles are similar by the SAS Similarity Postulate. A. 5 over 10 equals 5 over 2 and one half B. 5 over 10 equals 5 over 5 C. 10 over 5 equals 5 over 2 and one half D. 10 over 5 equals 2 and one half over 5

Which of the following best completes the proof

sarath30

11.12.2020

C. C. 10 over 5 equals 5 over 2 and one half

Step-by-step explanation:

Two ∆s are similar if their corresponding angles are congruent, and also if the ratio of their corresponding sides are equal.

If ΔWXZ ~ ΔXYZ, then,

$\frac{WX}{XY} = \frac{WZ}{XZ} = \frac{XZ}{YZ}$

Thus:

$\frac{WX}{XY} = \frac{10}{5} = \frac{5}{2.5} = 2$

Therefore, the proportion $\frac{10}{5} = \frac{5}{2.5}$ that shows the corresponding sides are proportional.

The answer is: C. 10 over 5 equals 5 over 2 and one half.

0,0(0 оценок)

tyreshagarrett123

29.06.2022

TO PROVE :-

$\frac{\tan \theta + \sin \theta}{\tan \theta - \sin \theta} = \frac{\sec \theta + 1}{\sec \theta - 1}$

SOLUTION :-

First of all , simplify L.H.S.

$\frac{\tan \theta + \sin \theta}{\tan \theta - \sin \theta}$

Use $\tan \theta = \frac{\sin \theta}{\cos \theta}$ in place of tanθ.

$= \frac{\frac{\sin \theta}{\cos \theta} + \sin \theta }{\frac{\sin \theta}{\cos \theta} - \sin \theta}$

Take sinθ common from both numerator & denominator.

$= \frac{\sin \theta (\frac{1}{\cos \theta} + 1) }{\sin \theta (\frac{1}{\cos \theta}- 1) }$

Cancel the sinθ from both numerator & denominator.

$= \frac{\frac{1}{\cos \theta} +1}{\frac{1}{\cos \theta} -1}$

Use $\sec \theta = \frac{1}{\cos \theta}$

$= \frac{\sec \theta + 1}{\sec \theta - 1}$

∴ L.H.S. = R.H.S

0,0(0 оценок)