In △TUV, TU¯¯¯¯¯¯¯ and TV¯¯¯¯¯¯¯ are bisected by WX¯¯¯¯¯¯¯¯¯¯ at W and X, respectively. Which of the following statements is true?(1 point)
WX=12TU
WX=12TV
UV=12WX
UV=2WX
To determine which of the given statements is true, we need to understand the given information. Let's break it down step by step:
1. In triangle △TUV, TU¯¯¯¯¯¯¯ and TV¯¯¯¯¯¯¯ are bisected by WX¯¯¯¯¯¯¯¯¯¯ at points W and X, respectively.
This means that the line segment TU is divided into two equal parts by the line WX, with point W as its midpoint. Similarly, the line segment TV is divided into two equal parts by the line WX, with point X as its midpoint.
Now, let's analyze the given statements:
Statement 1: WX = 12TU
Statement 2: WX = 12TV
Statement 3: UV = 12WX
Statement 4: UV = 2WX
To determine which statement is true, we can use the information that TU¯¯¯¯¯¯¯ is bisected by WX¯¯¯¯¯¯¯¯¯¯ at point W. Since the bisection divides TU into two equal parts, we can conclude that TX = UW. Similarly, since TV¯¯¯¯¯¯¯ is bisected by WX¯¯¯¯¯¯¯¯¯¯ at point X, we can say that TX = VX.
Now, let's analyze the statements using this information:
Statement 1: WX = 12TU. Since TX = UW, we can rewrite this statement as WX = 12TX which means WX is 12 times the value of TX. Since TX = VX, this statement would imply that WX is 12 times the value of VX, which is not necessarily true. So statement 1 is not necessarily true.
Statement 2: WX = 12TV. Using the same logic as before, we can rewrite this statement as WX = 12TX which means WX is 12 times the value of TX. Since TX = VX, this statement would imply that WX is 12 times the value of VX, which is not necessarily true. So statement 2 is not necessarily true.
Statement 3: UV = 12WX. Since we don't know the relationship between UV and WX, we cannot determine if this statement is true or not based on the given information. So statement 3 is inconclusive.
Statement 4: UV = 2WX. Similarly, since we don't know the relationship between UV and WX, we cannot determine if this statement is true or not based on the given information. So statement 4 is inconclusive.
Therefore, based on the given information, none of the statements can be determined to be true.
First learn to type fractions! Like 1/2
Since WX is parallel to UV, △TWX~△TUV and 1/2 the size