Are these triangles similar? if so, what postulate or theorem justifies that they are similar?

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

7 0

Answer:

Yes The triangles are similar by SAS Similarity Theorem

Step-by-step explanation:

we know that

<u>Side-Angle-Side Similarity,</u> states that If an angle of a triangle is congruent to an angle of another triangle and if the included sides of these angles are proportional, then the two triangles are similar

In this problem

Angle L is congruent with Angle Z

Verify if the included sides are proportional

$\frac{LJ}{ZY}=\frac{KL}{XZ}$

substitute the values

$\frac{3}{1.5}=\frac{4}{2}$

$2=2$ -----> is true

therefore

The triangles are similar by SAS

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The formula for the volume of a cone is V = jarh, where V is the volume, r is the radius, and h Is the heightWhat is the volume

olga nikolaevna [1]

Given:

The radius, r=4x

The height,

$h=21xy^2$

To find the volume of the cone:

The volume of the cone formula is,

$V=\frac{1}{3}\pi r^2h$

Substitute the values of r and h in the above formula we get,

$\begin{gathered} V=\frac{1}{3}\pi\times(4x)^2\times21xy^2 \\ =\frac{1}{3}\pi\times16x^2\times21xy^2 \\ =\pi\times16x^2\times7xy^2 \\ =112\pi x^3y^2 \end{gathered}$

Hence, the volume of the cone is