X^2-81 (answer using factoring polynomials)

Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ?

skelet666 [1.2K]

Angles formed by the segment $\overline{XZ}$ in the triangles ΔWXZ, and ΔXYZ, are equal and the given corresponding sides are proportional.

The option that best completes the proof showing that ΔWXZ ~ ΔXYZ is; <u>16 over 12 equals 12 over 9</u>

Reasons:

The proof showing that ΔWXZ ~ ΔXYZ is presented as follows;

Segment $\overline{XZ}$ is perpendicular to segment $\overline{WY}$

∠WZX and ∠XZY are right angles by definition of $\overline{XZ}$ perpendicular to $\overline{WY}$

∠WZX in ΔWXZ = ∠XZY in ΔXYZ = 90° (definition)

$\displaystyle \frac{WZ}{XZ} = \frac{16}{12} = \mathbf{ \frac{4}{3}}$

$\displaystyle \mathbf{ \frac{XZ}{ZY}} = \frac{12}{9} = \frac{4}{3}$

Therefore;

$\displaystyle \frac{16}{12} = \frac{12}{9}$ , which gives, $\displaystyle \mathbf{\frac{WZ}{XZ} }= \frac{XZ}{ZY}$

Given that two sides of ΔWXZ are proportional to two sides of ΔXYZ, and

that the included angles between the two sides, ∠WZX and ∠XZY are

congruent, the two triangles, ΔWXZ and ΔXYZ are similar by Side-Angle-

Side, SAS, similarity postulate.

The option that best completes the proof is therefore;

$\displaystyle \frac{16}{12} = \frac{12}{9}$ which is; <u>16 over 12 equals 12 over 9</u>

Learn more about the SAS similarity postulate here:

brainly.com/question/11923416

4 0

2 years ago

Which expressions are equal to 0 when x = -1? Check all that apply.

Sphinxa [80]

Answer:

A C and E

Step-by-step explanation:

6 0

3 years ago

A number raised to a negative exponent is negative. always never sometimes

Romashka [77]

It is negative only when the number itself is negative.
hence, sometimes.

8 0

3 years ago

Read 2 more answers

Find the lengths of the sides of the triangle PQR. P(4, 3, 4), Q(2, 1, 3), R(2, 7, 0) a. |PQ| = b. |QR| = c. |RP| =

Nat2105 [25]

Given :

Three points , P(4, 3, 4), Q(2, 1, 3), R(2, 7, 0) .

To Find :

The length of sides .

Given :

We know , length of two points P(x,y ,z) and Q(a,b,c) is given by :

$L=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}$

Length of PQ :

$PQ=\sqrt{(4-2)^2+(3-1)^2+(4-3)^2}\\\\PQ=\sqrt{4+4+1}=\sqrt{9}\\\\PQ=3$

Length of QR :

$QR=\sqrt{(2-2)^2+(1-7)^2+(3-0)^2}\\\\QR=\sqrt{0+6^2+3^2}\\\\QR=\sqrt{36+9}\\\\QR=\sqrt{45}\\\\QR=3\sqrt{5}$ :

Length of RP :

$RP=\sqrt{(2-4)^2+(7-3)^2+(0-4)^2}\\\\RP=\sqrt{2^2+4^2+4^2}\\\\RP=\sqrt{4+16+16}\\\\RP=\sqrt{36}\\\\RP=6$

Hence , this is the required solution .

4 0

3 years ago

Fraction multiplying by fractions

Amanda [17]

$\bf \cfrac{2}{9}\times a=\cfrac{3}{15}\implies \cfrac{2a}{9}=\cfrac{1}{5}\implies 2a=\cfrac{9\cdot 1}{15}\implies 2a=\cfrac{3}{5}
\\\\\\
a=\cfrac{3}{2\cdot 5}
\implies 
a=\cfrac{3}{10}\\\\
-------------------------------\\\\
\cfrac{2}{5}\times b=\cfrac{7}{12}\implies \cfrac{2b}{5}=\cfrac{7}{12}\implies 2b=\cfrac{5\cdot 7}{12}\implies 2b=\cfrac{35}{12}
\\\\\\
b=\cfrac{35}{2\cdot 12}\implies b=\cfrac{35}{24}$

3 0

2 years ago