segment tq is 26 units long. what is the length of qv? 8 units 26 units 31 units 32 units
segment tq is 26 units long. what is the length of qv? 8 units 26 units 31 units 32 units
Answer
Explanation:
Step1: Set up equation for x
Since the diagonals of a kite are perpendicular and one diagonal bisects the other, we can set up an equation using the given side - lengths. In a kite, the two non - congruent adjacent sides are equal. So, $3x + 2=4x - 1$. $3x+2 = 4x - 1$ $4x-3x=2 + 1$ $x = 3$
Step2: Analyze the property of kite's diagonals
The diagonal that is bisected by the other diagonal has equal segments on either side of the intersection. Diagonal $TV$ bisects diagonal $SQ$ at right - angles. Given $TQ = 26$ units, and the diagonal $TV$ is the perpendicular bisector of $SQ$, then $QR=RS$ and $TQ = QV$ (by the property of a kite's diagonals).
Answer:
B. 26 units