How to find if right triangles are similar

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SSAT Upper Level Quantitative › How to find if right triangles are similar

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If a right triangle is similar to a right triangle, which of the other triangles must also be a similar triangle?

$\frac{1}{3}-\frac{1}{4}-\frac{1}{5}$

$\frac{1}{6}-\frac{1}{8}-\frac{1}{10}$

Explanation

For the triangles to be similar, the dimensions of all sides must have the same ratio by dividing the 3-4-5 triangle.

The 6-8-10 triangle will have a scale factor of 2 since all dimensions are doubled the original 3-4-5 triangle.

The only correct answer that will yield similar ratios is the triangle with a scale factor of 4 from the 3-4-5 triangle.

The other answers will yield different ratios.

What is the main difference between a right triangle and an isosceles triangle?

A right triangle has to have a $90^{\circ}$ angle and an isosceles triangle has to have equal, base angles.

An isosceles triangle has to have a $90^{\circ}$ angle and a right triangle has to have equal, base angles.

A right triangle has to have a $50^{\circ}$ angle and an isosceles triangle has to have equal, base angles.

A right triangle has to have a $90^{\circ}$ angle and an isosceles triangle has to have equal, base angles.

Explanation

By definition, a right triangle has to have one right angle, or a $90^{\circ}$ angle, and an isosceles triangle has equal base angles and two equal side lengths.

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