Question

Given: PQ ≈ QS and QS = ST
Prove: PQ = ST
Proof:

Answer 1

To prove that PQ = ST, we can use the given information and mathematical reasoning.

Step-by-step explanation:

To prove that PQ = ST, we need to use the given information and apply some mathematical reasoning. Since PQ ≈ QS and QS = ST, we can show that PQ = ST. Here's how:

Since PQ ≈ QS, it means that the length of line segment PQ is approximately equal to the length of line segment QS.

Since QS = ST, it means that the length of line segment QS is exactly equal to the length of line segment ST.

Combining these two statements, we can conclude that the length of line segment PQ is approximately equal to the length of line segment ST. Therefore, PQ = ST.

Answer 2

Proof:

Using the given information, we know that PQ is approximately equal to QS and QS is exactly equal to ST.

Since a value that is approximately equal to another value can be treated as equal in many cases, we can say that PQ is roughly equal to ST.

To prove that PQ is exactly equal to ST, we must use the transitive property of equality.

Transitive Property of Equality: If a = b and b = c, then a = c.

Using the transitive property, we can say:

PQ ≈ QS and QS = ST → PQ ≈ ST

Since PQ is approximately equal to ST and they have the same units of measurement, we can round the values to the same number of decimal places and say:

PQ ≈ ST ≈ rounded value

Therefore, PQ is exactly equal to ST because they have the same rounded value.