a Can you find any parallel sides in the triangular faces?
B
b In an isosceles triangle, the vertex angle is
A
a ∠V and ∠UXV
B
b 8 m
Practice makes perfect
a We already know that the angles of the triangular faces, △ WUX and △ XVY, are congruent. Therefore, the vertex angle of △ XVY, which we have labeled below as ∠V, is congruent to ∠WUX.
To find a second congruent angle, we have to consider the remaining angles of the triangular faces. Since â–³ WUX and â–³ XVY are both congruent and isosceles, their base angles will be the same.
Since the base angles are congruent, and they both sit on a straight line WY, we know the following.
WU ∥ XV
If we view XU as a transversal, we can identify ∠WUX and ∠UXV as alternate interior angles. According to the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then the pair of alternate interior angles are congruent.
This means we can also identify ∠UXV as congruent with ∠WUX.
b Let's mark the distance UV in our diagram. Note that WX≅ XY and therefore, we can mark XY as 8 m since it's congruent corresponding side is WX.
In any isosceles triangle, the height bisects the base. Let's add this piece of information to the diagram.
As we can see, UV is half the base of each triangle. Therefore, the distance between the points U and V is
4 m+4 m=8 m
