We don't have any required textbook for this college course so I can only post part of my lecture notes, which are really short since I've only had my first class...
If P = P[sub:1ux2z08h]1[/sub:1ux2z08h]+P[sub:1ux2z08h]2[/sub:1ux2z08h]+...+P[sub:1ux2z08h]n[/sub:1ux2z08h], Q=Q[sub:1ux2z08h]1[/sub:1ux2z08h]+Q[sub:1ux2z08h]2[/sub:1ux2z08h]+...+Q[sub:1ux2z08h]n[/sub:1ux2z08h], where P and Q stand for the area of polygons P and Q respectively
and P[sub:1ux2z08h]i[/sub:1ux2z08h]is congruent to(I can't type the sign of congruence here)Q[sub:1ux2z08h]i[/sub:1ux2z08h] for 1<=i<=n, we say that P and Q are congruent by addition and we write P is congruent to Q(+)
If there exist R,S,U[sub:1ux2z08h]1[/sub:1ux2z08h],...,U[sub:1ux2z08h]n[/sub:1ux2z08h], V[sub:1ux2z08h]1[/sub:1ux2z08h],...,V[sub:1ux2z08h]n[/sub:1ux2z08h] such that R=P + U[sub:1ux2z08h]1[/sub:1ux2z08h] + U[sub:1ux2z08h]2[/sub:1ux2z08h]+...+U[sub:1ux2z08h]n[/sub:1ux2z08h], Q=Q + V[sub:1ux2z08h]1[/sub:1ux2z08h]+V[sub:1ux2z08h]2[/sub:1ux2z08h]+...+V[sub:1ux2z08h]n[/sub:1ux2z08h],
and U[sub:1ux2z08h]i[/sub:1ux2z08h]is congruent to(I can't type the sign of congruence here)V[sub:1ux2z08h]i[/sub:1ux2z08h] for 1<=i<=n, and R is congruent to S(+) we say that P and Q are congruent by subtraction and we write P is congruent to Q(-)
Quest: Show that 2 parallelograms having the same base and equal altitudes are equivalent.
I understand that we are to show either they are congruent by addition or congruent by subtraction. However, I have no idea which one is applicable in this case and what kind of approach should I use to go about doing this...Perhaps just give me clues on how to start to get me thinking, any aid of diagrams will be greatly appreciated...Thank you!
If P = P[sub:1ux2z08h]1[/sub:1ux2z08h]+P[sub:1ux2z08h]2[/sub:1ux2z08h]+...+P[sub:1ux2z08h]n[/sub:1ux2z08h], Q=Q[sub:1ux2z08h]1[/sub:1ux2z08h]+Q[sub:1ux2z08h]2[/sub:1ux2z08h]+...+Q[sub:1ux2z08h]n[/sub:1ux2z08h], where P and Q stand for the area of polygons P and Q respectively
and P[sub:1ux2z08h]i[/sub:1ux2z08h]is congruent to(I can't type the sign of congruence here)Q[sub:1ux2z08h]i[/sub:1ux2z08h] for 1<=i<=n, we say that P and Q are congruent by addition and we write P is congruent to Q(+)
If there exist R,S,U[sub:1ux2z08h]1[/sub:1ux2z08h],...,U[sub:1ux2z08h]n[/sub:1ux2z08h], V[sub:1ux2z08h]1[/sub:1ux2z08h],...,V[sub:1ux2z08h]n[/sub:1ux2z08h] such that R=P + U[sub:1ux2z08h]1[/sub:1ux2z08h] + U[sub:1ux2z08h]2[/sub:1ux2z08h]+...+U[sub:1ux2z08h]n[/sub:1ux2z08h], Q=Q + V[sub:1ux2z08h]1[/sub:1ux2z08h]+V[sub:1ux2z08h]2[/sub:1ux2z08h]+...+V[sub:1ux2z08h]n[/sub:1ux2z08h],
and U[sub:1ux2z08h]i[/sub:1ux2z08h]is congruent to(I can't type the sign of congruence here)V[sub:1ux2z08h]i[/sub:1ux2z08h] for 1<=i<=n, and R is congruent to S(+) we say that P and Q are congruent by subtraction and we write P is congruent to Q(-)
Quest: Show that 2 parallelograms having the same base and equal altitudes are equivalent.
I understand that we are to show either they are congruent by addition or congruent by subtraction. However, I have no idea which one is applicable in this case and what kind of approach should I use to go about doing this...Perhaps just give me clues on how to start to get me thinking, any aid of diagrams will be greatly appreciated...Thank you!