Question

(a)R340s34°TUVPart AHow do you know the triangles are similar?00BU SE ZA

Answer 1

Two triangles are similar if the measures of two angles in the first triangle are equal

Let us check this rule in the given figure

In triangles TRV and TSU

`m\angle TRV=m\angle TSU=\text{ 34 degree}`
`m\angle RTV=m\angle STU=90\text{ degrees}`

Then the two triangles are similar because two angles in the 1st triangle equal two the corresponding angles in the 2nd triangle

When the two triangles are similar their corresponding sides are proportional, then

`(RT)/(ST)=(RV)/(SU)=(TV)/(TU)`

That means the corresponding sides have equal ratio

Since the triangles have a different scale, one triangle is larger than the other by a constant value

Then the transformation is dilation

You will multiply the sides of one triangle by a scale factor to get the sides of the other triangle

The transformation is dilation