which statement is true about the diagram? 10 5 4 a k b t o k is the midpoint of ab. o b is the midpoint of…
which statement is true about the diagram? 10 5 4 a k b t o k is the midpoint of ab. o b is the midpoint of kt. o ak = bt o ab = kt
Answer
Explanation:
Step1: Calculate length of segments
From the diagram, $AK = 5$, $KB=5$, $BT = 4$. So $AB=AK + KB=5 + 5=10$, $KT=KB + BT=5 + 4 = 9$.
Step2: Check each statement
- For “$K$ is the mid - point of $\overline{AB}$”: Since $AK = KB = 5$ and $AB=10$, by the definition of mid - point (a point that divides a line segment into two equal parts), $K$ is the mid - point of $\overline{AB}$.
- For “$B$ is the mid - point of $\overline{KT}$”: Since $KB = 5$ and $BT=4$, $KB\neq BT$, so $B$ is not the mid - point of $\overline{KT}$.
- For “$AK = BT$”: Since $AK = 5$ and $BT = 4$, $AK\neq BT$.
- For “$AB = KT$”: Since $AB = 10$ and $KT=9$, $AB\neq KT$.
Answer:
$K$ is the midpoint of $\overline{AB}$.