Answer:
1) triangles are similar
Step-by-step explanation:
The height from vertex X of isosceles ∆WXY is 4 units. The width WY is also 4 units. In isosceles ∆UVW, the height from vertex V is 6 units, and the width UW is also 6 units.
The height ratios are ...
∆WXY/∆UVW = 4/6
The width ratios are ...
∆WXY/∆UVW = 4/6
The measures of ∆WXY are proportional to those of ∆UVW, so the triangles are similar.
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Strictly speaking, you cannot go by triangle height and width alone. That is why we made not of the fact that the triangles are <em>isosceles</em>. When base and height of an isosceles triangle are proportional, the Pythagorean theorem guarantees that side lengths are proportional. Trigonometry can also be invoked to support the claim that angles are congruent.
