기하학및연습 Greenberg - Euclidean and Non-Euclidean Geometries - Development and History 3e (WHF, 1993) 문제풀이(1-4)

b) Adjacent sides of quadrilateral

- Two sides of a quadrilateral which have a common end point - are called its adjacent sides. 

 

c) Opposite sides of quadrilateral

Two sides 05 a quadrilateral are called its opposite sides if they

do not have a common end point. 

 

d) The diagonals of quadrilateral

Two diagonals of a convex quadrilateral are the line segments

that connect Opposite vertices 

 

e) A parallelogram 

 A parallelogram is a quadrilateral with opposite side parallel

(and therefore opposite angles equal)

 

 4. Define vertical angles (Figure 1.21). How would you attempt to prove that vertical angles are congruent to each other? - (Just sketch a plan for a proof - don't carry it out in detail) 

Vertical angles are the angles opposite each other when the lines cross. "Vertical" in this case we means they share the same Vertex (corner point), not the usual meaning of up-down

 

1. draw two lines which are parallel

2. a =a', b=b' 

3, those two angles which share some vertex are same.