Question

If Triangle RST similar to Triangle xyz
and
RS: X Y
3/5 then ST : YZ = ?​

Answer 1

Answer:

3/5 ( 3 : 5 ) is the ratio of side ST and YZ

Step-by-step explanation:

Corresponding parts of ∆RST and ∆XYZ

• RS ⟷ XY
• ST ⟷ YZ
• RT ⟷ XZ
• ∠R ⟷ ∠X
• ∠S ⟷ ∠Y
• ∠T ⟷ ∠Z

RS and XY are corresponding sides, and their ratio is given as 3:5, ST and YZ are also corresponding sides of similar triangle, so, there is a will be same as that of RS and XY i.e. 3 : 5 (3/5)

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If two triangles are similar, then the corresponding angles are congruent/equal and corresponding sides of the similar triangle size up or sized down by the same factor.

In other words, similar triangles have all corresponding angles equal and corresponding sides are scaled by the same factor i.e. we multiply sides of one triangle by a constant k to get the sides of other triangle.

Answer 2

Given:-

ΔRST ≈ Δ XYZ

RS : XY  = $\sf\dfrac{3}{5}$

To Find:-

ST : YZ ?

Solution:

ΔRST ≈ Δ XYZ

Similar Triangles:-

❍ If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

❍ Corresponding angles are congruent and the corresponding sides are proportional.

$\longrightarrow\sf\dfrac{RS}{XY} = \dfrac{ST}{YZ} = \dfrac{RT}{XZ}$

$\longrightarrow\sf\dfrac{RS}{XY} = \dfrac{3}{5}$

$\longrightarrow\sf\dfrac{ST}{YZ} = \dfrac{RT}{XZ} = \dfrac{3}{5}$

$\longrightarrow\sf\dfrac{ST}{YZ} = \dfrac{3}{5}$

$\implies$ ST : YZ  = $\sf\dfrac{3}{5}$