Chapter 8.4, Problem 5PSA

To determine

To show that product of two sides are equal.

Answer to Problem 5PSA

  $ProductofNOandRTisequaltoproductofRSandNP.$

Explanation of Solution

Given information:

  $\Delta NOP~ \Delta RST$

Formula used:

The below properties are used:

Corresponding sides of similar triangles are proportional.

Means extremes product theorem:

If a product of a pair of not zero numbers is equal to the product of another pair of not zero numbers, then either pair of numbers be made the extremes, and the other pair the means, of proportion.

Proof:

  

It is given that,

  $\Delta NOP~ \Delta RST$

Corresponding sides of similar triangles are proportional.

  $NO/RS=NP/RT$

Applying means extremes product theorem, we get

  $NO.RT=RS.NP$