 Hello and how are you all today? My name is Priyanka and the question says in each of the following give the justification of the constructions also Now here the first construction we are dealing with today is draw a line segment of length 7.6 centimeter and divide it in the ratio five is to eight measure the two parts now We have already written down the steps of construction for you I'll be reading one and the other steps one by one and drawing the diagram Simultaneously now the first step of construction is to draw a line segment AB of length 7.6 centimeter So let us draw a line segment of length 7.6 centimeter Right now the next step is to draw a ray AX Making an acute angle with AB and then draw a ray BY parallel to AX by making angle ABY equal to angle Bax so what we need to do is we need to make equal angles measuring equal angles at A and B and The ray that we are drawing will be named as This is AX and this is BY the angles x AB is Equal to ABY right now we need to locate the points Five points since we need to divide it in ratio five is to eight Therefore our M will be five and N will be eight so on a we will be marking five equal parts And on B will we will be marking eight equal parts such that all the parts are equal to each other So here we have to draw five equal parts So this let it be one two three four five Let us name it as a one a two a three a four and a Five and a a one is equal to a one a two is equal to a two that means all these Subparts are equal to each other in the same way. We will be marking on B We need to mark eight equal parts over here. So one two three four five six seven eight Let us name it as B1 B2 B3 B4 B5 B6 B7 B8 You can mark these equal points with the help of the compass and do remember that the radius of the compass should not change While marking all the points on AX as well as on BY now we need to divide this line segment into In the ratio five is to eight. So we will be Joining a five to B eight and let it intersect at AB at point C And then AC is to CB will be equal to five is to eight, right? So what we need to do next is we need to join a five to be eight and The point of intersection on AB. Let us name it as C So AC is to CB is in ratio five is to eight Now for justification What we need to do is we will be measuring AC and CB separately This is equal to two point nine centimeter, and this is equal to 4.7 centimeter and And this is the length of AC and CB respectively Right and we can see that AC is to CB is in ratio five is to Eight right so this completes the session. Hope you understood the solution Well, do make your construction need and Don't forget to write down the steps of construction neatly. Have a very nice day ahead