Assertion: Through two distinct points passes a unique line. Two lines are said to be [i]distinct[/i] if there is at least one point that belongs to one but not the other. Otherwise, we say the lines are the same. Lines that have no point in common are said to be [i]parallel[/i].[br][br]Therefore, we can conclude: given two distinct lines, either they are parallel, or they have exactly one point in common.
Label the triangles [math]WXY[/math] and [math]DEF[/math], so that angle [math]W[/math] is congruent to angle [math]D[/math], angle [math]X[/math] is congruent to angle [math]E[/math], and side [math]WX[/math] is congruent to side [math]DE[/math].[br][br]Use a sequence of rigid motions to take triangle [math]WXY[/math] onto triangle [math]DEF[/math]. For each step, explain how you know that one or more vertices will line up.[br]
[size=150]By definition, that means that segment [math]AB[/math] is parallel to segment [math]CD[/math], and segment [math]BC[/math] is parallel to segment [math]AD[/math].[br][br][list][*][size=100]Use the applet below. Sketch parallelogram [math]ABCD[/math] and then draw an auxiliary line to show how [math]ABCD[/math] can be decomposed into 2 triangles.[br][/size][/*][*][size=100]Prove that the 2 triangles you created are congruent, and explain why that shows one pair of opposite sides of a parallelogram must be congruent.[/size][/*][/list][/size]
How many ears does a parallelogram have?[br]