Question

These two scalene triangles are similar with a scale of 2:3. What is true about these figures?

Answer 1

Answer:

PQ/GH = 3/2

Step-by-step explanation:

Answer 2

The fourth option is correct because $\dfrac{PQ}{GH}=\dfrac{3}{2}$.

Given:

The triangles GHI and PQR are similar with a scale of $2:3$.

To find:

The true statement about given figures.

Explanation:

The corresponding sides of similar triangles are proportional and the corresponding angles are congruent.

$\dfrac{GH}{PQ}=\dfrac{HI}{QR}=\dfrac{GI}{PR}=\dfrac{2}{3}$

$\angle G\cong \angle P$

$g=p$

$\dfrac{g}{p}=1$

So, the third option is incorrect.

$\angle H\cong \angle Q$

$h=q$

$\angle I\cong \angle R$

$i=r$

$\dfrac{i}{r}=1$

So, the second option is incorrect.

Now,

$\dfrac{HI}{QR}=\dfrac{2}{3}\neq \dfrac{3}{2}$

So, the first option is incorrect.

$\dfrac{PQ}{GH}=\dfrac{3}{2}$

Therefore, the fourth option is correct.

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