Measurement of Segments (Level 2) | Examples I

mathfortress (58)in #geometry • 7 years ago

Measurement of Segments (Level 2) | Examples I

In this post we will start taking a look at simple examples that require us to find the length of segments and use the concept of congruent segments. Before we start a word of caution from this point on I will be assuming that you are very well versed with the basic concepts and skills learned in a typical Algebra I or beginning algebra course. You should be comfortable solving equations with a single variable, solving systems of equations with 2 variables, working with fractions and decimals and translating word problems into equations. If you are a bit rusty I recommend you brush up on these skills before proceeding. With that said let’s go ahead and take a look at the first example.

In this problem we are provided with a number line that contains various points. Each point has a particular coordinate. We are asked to name three segments that are congruent to segment PQ. Recall that congruent segments have the same length. We first need to figure out the measurement of segment PQ before we determine which other segments are congruent to this segment. The coordinate of point P and point Q is negative 2 and negative 1 respectively. Taking the absolute difference of both coordinates and simplifying we obtain 1 for the length of segment PQ.

Now that we know the length of segment PQ let’s go ahead and find three other line segments that have same length. One line segment that has a length equal to 1 would be line segment QR, another one would be line segment RS and the last one would be line segment ST. So these three line segments would be congruent to segment PQ.

Alright let’s try the next example.

In this problem we are given the coordinates of two points and we are asked to determine the distance between the points. Notice that in this problem we are not provided with a diagram or figure. We are going to have to draw it ourselves. So let’s go ahead and draw a number line and use point A to represent the point located at the coordinate negative 2 and use point B to represent the coordinate located at positive 6.

Now that we have this visual as a guide, we can go ahead and find the length between point A and point B. Similar to the previous problem we go ahead and find the absolute difference between the points coordinates, doing that and simplifying we obtain 8 as our answer. Notice that in some geometry problems you will be responsible for drawing the diagram of the problem, at times you can get away with not drawing the diagram, I personally do not recommend it.

Ok let’s try the next problem.

Here we are provided with a number line that includes various points. We are asked to name the point on ray DA whose distance from point D is 2. Let’s start by drawing ray DA. Next we need to determine the point that is 2 units away from point D. Starting from point D and moving in the same direction as ray DA we see that point B is 2 units away from point D. So point B is our final answer.

Let’s try the next problem.

Similar to the previous problem we want to determine the point whose distance is 2 units away from point D and is located on ray DG. So we start from point D and move in the direction of ray DG, we see that point F is 2 units away from point D so point F is our final answer.

Let’s take a look at the next example.

Now we need to determine which two points are 2 units away from point E. Since we can only move either left or right in a number line all we need to do is to find the points that are 2 units away from both directions. Starting at point E and moving 2 units to the left we see that point C is located 2 units away from point E. In the same manner starting from point E and moving 2 units to the right we see that point G is located 2 units away from point E. So point C and point G is our final answer.

Let’s move along to the next example.

Now we need to determine which segment is congruent to segment AF, first let’s determine the length of segment AF, so we take the coordinate of point A and point F and use them to compute the length, taking the absolute value of the difference of these coordinates and simplifying we obtain 5.

Now we need to find a line segment that also has a length of 5. Notice that the only way to get another line segment with a length of 5 is by moving segment AF 1 unit to the right. This new line segment has point B and point G as end points. So a line segment that is congruent to segment AF is segment BG. So this is our final answer.

Alright let’s try the next example.

In this problem we are provided with a partially labeled number line and we are asked to find the length of segment PQ, we can easily determine the length by finding the distance between Point P and point Q recall that we can determine this in a couple of ways. We can use the number line to count the distance from one end point to the other end point. We can also find the absolute difference between each of points coordinate. Regardless of how we decide to find the length the measurement of segment PQ is equal to 5.

Let’s go over the final example.

The next problem is asking us to explain why line segment PQ is not congruent to line segment QR when the coordinate of point R is equal to 7.

Recall that two line segments are considered to be congruent if they have the same length or measurement. We know from the previous problem that the length of line segment PQ is equal to 5. Let’s go ahead and find the length of line segment QR by using the coordinates of the end points.

Finding the length and simplifying we obtain 4 for the length of segment QR, since the length of both line segments are not the same we can conclude that segment PQ is not congruent to segment QR. We can denote this symbolically by using the congruent symbol with a forward slash going across it, this is similar to the “does not equal” symbol introduced in your beginning algebra course.