Question

Given: t ( - 4 , - 1 ) , r ( - 2 , 5 ) , a ( 4 , 8 ) , and p ( 8 , 5 ) are vertices of quadrilateral trap . prove: trap is a trapezoid. statements reasons 1. t ( - 4 , - 1 ) , r ( - 2 , 5 ) , a ( 4 , 8 ) , and p ( 8 , 5 ) are vertices of quadrilateral trap . 1. given 2. slope of tr : 5 - ( - 1 ) - 2 - ( - 4 ) = 3 , slope of ra : 8 - 5 4 - ( - 2 ) = 1 2 , slope of ap : 5 - 8 8 - 4 = - 3 4 , slope of pt : - 1 - 5 - 4 - 8 = 1 2 2. definition of slope 3. ? 3. ? 4. trap is a trapezoid. 4. definition of a trapezoid what is step 3 to complete the proof?

1) ra || pt by the definition of parallel lines
2) tr ⊥ ra by the definition of perpendicular lines
3) tr || ap by the definition of parallel lines
4) ap ⊥ ra by the definition of perpendicular lines

Answer 1

In this proof, step 3 involves showing that TR is parallel to AP. The given slopes of TR and AP allow us to conclude that TR and AP are parallel, making the quadrilateral TRAP a trapezoid.

Step-by-step explanation:

Step 3 to complete the proof is: tr || ap by the definition of parallel lines. The definition of a trapezoid states that in a trapezoid, one pair of opposite sides is parallel. From the given slopes, we can see that the slope of TR is 3 and the slope of AP is -3/4. Since the slopes are equal, we can conclude that TR and AP are parallel, making the quadrilateral TRAP a trapezoid.