Question

which descriptions from the list below accurately describe the relationship between △ xyz and △ uvw? check all that apply.
(there are two triangles in the image, △ xyz with sides 3, 4, 5 and angles 37°, 53°, 90°; △ uvw with sides 6, 8, 10 and angles 37°, 53°, 90°. the options are: same shape, congruent, similar, same size)

Explanation:

Step1: Check Angle Correspondence

In $\triangle XYZ$ and $\triangle UVW$, the angles are $37^\circ$, $53^\circ$, and $90^\circ$ (since $37 + 53 + 90 = 180$). So, corresponding angles are equal, meaning they have the same shape.

Step2: Check Side Ratios

For $\triangle XYZ$: sides are $3, 4, 5$. For $\triangle UVW$: sides are $6, 8, 10$. The ratios are $\frac{6}{3} = 2$, $\frac{8}{4} = 2$, $\frac{10}{5} = 2$. So, sides are in proportion (scale factor 2), so they are similar.

Step3: Check Congruence and Same Size

Congruent triangles have equal sides (same size), but here sides are scaled by 2, so not congruent or same size.

Answer:

Same shape, Similar