View Recognition (Top-Front-End):
In this subsection of the PAT, there are three view points of a solid object presented in each question as illustrated in the following question. The view looking down on the object is in the upper left-hand corner of the illustration (top view). The view looking at the object from the front is in the lower left-hand corner (front view). The view looking at the object from the right side is in the lower right-hand corner (end view). The views are without perspective, meaning the points in each of the viewed surfaces are viewed along parallel lines of vision.
Meaning of Solid Lines and Dotted/Dashed Lines: Solid lines drawn in different views represent a line that can be seen from that view. Dotted/Dashed lines represent a line that cannot be seen from that view but rather they are behind what you are seeing from that view.
Line Matching: Line matching strategy is figuring out which line corresponds to which and where a line would be in a given view in comparison with another view, it helps us find out which line corresponds to which change of elevation.
Here we have a step by step identification of what each solid and dotted/dashed lines represent in the views. In the following example you can see that the gap in the object is shown by dotted purple lines in the front and end view. This is a simple shape in a top front end view question that covers simple aspects that are shown in different views of a shape.
In another example, we have a cube inside out shape which is shown by solid lines in top view and dotted lines in other views since the lines of this cube would be invisible in front and end views. There is also an indentation that looks like L in the front view and since it is outside our shape is shown by solid lines.
You can study each view with respect to the 3D shape presented below for a better spatial perception of each view and how the dotted and solid lines are shaped.
Continue to make sure that all the shaded parts correspond to the answer choice in order to determine the correct one. Through process of elimination and observation you can decide which choice is correct and which is not.
Drawing Lines Strategy: Another strategy is drawing lines from the two views given to view that we want to find like the picture below. Here is our example shape shown by drawing lines between different views. Each of these pairs can be related to one another by drawing vertical lines to help us with our understanding of the view of the object, as you can see here it is shown by colored lines. Notice our end view is rotated 90 degrees counter clockwise. If rotation of one view confuses you then you can just draw curves instead of direct lines.
We are going to solve this question for practicing how to implement the strategies we have learned.
In this question we have to figure out the top view and we have 4 options plus front and end views of the object. We start by drawing the lines in our mind to imagine how the top view is going to be. If we draw lines from the solid lines as shown in the picture below we will find out we are going to have a square shape in our top view, but unfortunately it will not help us eliminate any of the options since they are all square shapes.
The vertical lines in front and end view can help us find out what the lines look like in top view so we are looking for vertical lines in front and end view to draw and match them in top view.
Don’t get confused by different lines, use each color separately in this example to make what you are imagining stand out. Consider the green lines only, they show the basic outer lines on the edges of the shape. You should start by drawing the green lines to get the overall outline shape of the view. If you do that you will have the orange shape. Now that these two colors are out of the way so are the outer edges and the overall outline of our shape. We proceed to drawing lines for the parts of the shape that go inside or on top of the shape like indentations and pegs and so on. We do this by drawing red and blue colored lines from each peg or indentation in the two views that we have to the view that we want to find out.
Based on the front view we can see that there is gap in the middle of the shape, in the shape of an upside down triangle. In option A, on the left side of the top view there is no solid line on the left side of the top view, which doesn’t match with other views so option A is incorrect.
In option B, there is no solid line in the middle of the top view which would make the middle of our upside down triangle but there is no solid line, so option B is incorrect as well.
In option C there is an extra solid line from left to right in the top view which doesn’t exist in front and end views and since solid lines represent an edge that is visible in each view but we can’t find any dotted or solid lines corresponding to this extra line in other views so option C is incorrect as well.
Therefore the correct answer is option D.
Shared Borders: Next step in drawing lines strategy is to decide on the shared solid lines of the different views. Notice that we draw these lines based on shared borders these views have with each other. The shared border in front and top view is shown by red color in the picture below.
Top line of the end view coordinates with right part of the top view as shown by the blue color in the picture above.
So if we draw the lines from the shared border of front to top view, and also from the shared border of end to top view to see how it would look like, we can expect a picture like the following.
Also, considering the fact that the right square in the front view is dotted, the corresponding line should not be touching the lowest line in the top view. Therefore, option A is incorrect. Likewise, when the left square in the front view is shown by solid lines, its corresponding line in the top view touches the lowest line in this view. So options B and C are incorrect.
Elimination Based on Unique Features: In this strategy we are looking for something unique about the two sides presented and then determining what that feature would look like in the view we are looking for. We are looking for something like a hole or a peg or something like that then we eliminate the answer choices that don’t match with that feature, and then do it again until you find the answer.
Here we have another problem to solve, for this one we first draw the outer boundaries which would make a shape like this:
Here we have a very good strategy regarding indentations that stick out of a shape.
Here we solve this question considering the peg that is a distinguishing feature only and eliminating options based on this unique feature.
Based on the front and end views we can see that the peg should be in sticking out on the right side of the front view and on the bottom side of the right side of this view, therefore options A and D are incorrect; in option A the peg is inside of the shape rather than sticking out from the right side and in option D the peg is on the top side of the right side rather than being on the bottom. We know the peg can’t be on top side of the right side in the top view like option D since there is a dotted line in front view in the place that peg is connected to the shape which indicates this peg is sticking out from this side. Also in the end view we can see the location of the peg can’t be like shown in option D.
Now we have to find out the difference between options B and C and which one is correct. The difference between B and C options is a dotted line in the location that the peg is connected to the shape. There must be a dotted line in this location in top view since the line that exists beneath the peg from the top view must be represented. Therefore option C is the correct answer.
Remember that holes that go through the object are visible as solid lines in one view and as dotted lines in the other two views. The following example illustrates this point.
Line Counting: This method is one of the obsolete strategies for answering view recognition questions, this strategy involves counting the dotted/dashed and solid lines in the view of a shape in question and then through elimination process you can figure out the correct answer.
In this method, vertical lines (both solid and dotted lines) in front view, must be the same number as the vertical lines in top view. Also the number of vertical lines in end view must be the same number as horizontal lines in top view. It is worth mentioning that any kind of indentation is considered a line (look at the following shape).
Therefore, the answer is A.
But this method was considered a short cut by test makers and therefore question designers now design questions in a way that you can no longer use this strategy to find the answers to the questions.
This section is very challenging and it is advised that you do at least 20 questions every day. It is important that you practice with solving as many of these questions as you can so that you get familiar with different shapes, views, and objects, and also to become faster to better manage your time on the real DAT.
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