Example Question - corresponding sides
Here are examples of questions we've helped users solve.
Finding Scale Factor of Similar Triangles
The image contains two similar right-angled triangles, Triangle CDE and Triangle VUW. We are given the lengths of the sides of each triangle, with side CD being 10 units, DE being 12 units, and CE being unknown but corresponding to side VW which is 9.6 units. We are asked to find the scale factor from Triangle CDE to Triangle VUW. The scale factor is the ratio of the lengths of corresponding sides in similar figures. To determine the scale factor between these two triangles, we can take the lengths of any pair of corresponding sides and divide them. Here, we can use DE and UW since those are the only two corresponding sides both of which we know the lengths. Since DE is the longer side in the larger triangle, we will divide the length of DE by the length of UW to get the scale factor. Let's do the calculation: Scale factor = (Length of DE in Triangle CDE) / (Length of UW in Triangle VUW) Scale factor = 12 / 9.6 When you divide 12 by 9.6, the result is: Scale factor = 1.25 This means that Triangle CDE is 1.25 times larger than Triangle VUW, or in other words, Triangle VUW is 1.25 times smaller than Triangle CDE. The scale factor is 1.25.
Determining Scale Factor Between Two Triangles
The image shows two similar triangles, triangle CDE and triangle VUW, with corresponding side lengths marked. Side CD is 10 units, side DE is 12 units, and side UW is given as 9.6 units. We are asked to find the scale factor. To find the scale factor between the two triangles, we compare the corresponding sides. Since the image shows side DE of triangle CDE corresponding to side UW of triangle VUW, and Triangle VUW is the smaller one, we can determine the scale factor by dividing the length of side UW by the length of side DE. Scale Factor = Length of side UW / Length of side DE Plugging in the given values: Scale Factor = 9.6 / 12 Scale Factor = 0.8 Therefore, the scale factor is 0.8.
Determining Scale Factor of Similar Figures
The given image shows two similar figures (triangles), and we are asked to find the scale factor between them. To determine the scale factor, we compare the lengths of corresponding sides of the similar figures. From the image, we observe that side CD in the larger figure corresponds to side UV in the smaller figure. We can calculate the scale factor (k) by dividing the length of UV by the length of CD: k = UV / CD k = 9.6 / 12 To solve for k, we divide 9.6 by 12: k = 0.8 So, the scale factor between the two similar figures is 0.8.
Finding Scale Factor Between Two Figures
The image shows two similar figures, and we are tasked with finding the scale factor. To find the scale factor from one figure to another, you can divide the lengths of corresponding sides. In the image, you can use the lengths of sides DC and UV to determine the scale factor. DC is 5 units long, and UV is 4 units long, both representing the shortest sides of their respective figures. To find the scale factor from the larger figure (DC) to the smaller one (UV), divide the length of UV by the length of DC: Scale factor = UV / DC Scale factor = 4 / 5 Scale factor = 0.8 Therefore, the scale factor from figure DC to figure UV is 0.8.
Finding Scale Factor of Similar Triangles
The image shows two similar triangles. When two triangles are similar, their corresponding sides are proportional, meaning the ratio between the lengths of one pair of corresponding sides is the same as the ratio between the lengths of any other pair of corresponding sides. To find the scale factor from the larger triangle CDE to the smaller triangle VTU, we divide the lengths of one pair of corresponding sides from the two triangles. We can use sides DE and TU for this purpose: Scale factor = side TU / side DE Scale factor = 8 / 12 Scale factor = 2 / 3 So, the scale factor from triangle CDE to triangle VTU is 2/3.
Calculating Scale Factor Between Two Triangles
The image shows two similar triangles with corresponding side lengths given. To find the scale factor, we can divide the length of a side of one triangle by the corresponding side length of the other triangle. From triangle CDE: CD = 10 DE = 12 CE = 5 From triangle VUT: VU = 9.6 UT = 8 VT = ? (we don't know this length, and we don't need it to find the scale factor). Let's use the sides CD and VU for our calculation since both of these corresponding sides are given: VU (from triangle VUT) / CD (from triangle CDE) = 9.6 / 10 = 0.96 Therefore, the scale factor from triangle CDE to triangle VUT is 0.96.
Solving for Missing Side Length in Similar Triangles
To solve for the missing side length in similar triangles, we can set up a proportion based on the corresponding sides of the triangles. Let's call the missing side length "x". For the smaller triangle, we have the sides as x (the one we want to find) and 8. For the larger triangle, the corresponding sides are 7 and 16. Setting up our proportion, we get: x/7 = 8/16 Now we want to solve for x: x = (8/16) * 7 x = (1/2) * 7 x = 7/2 x = 3.5 So the missing side length is 3.5 units.
Congruent Triangles and Side Lengths
The image shows a pair of congruent triangles, ΔDEG and ΔEFG, with DE congruent to EF, DG equal to 3a, and FG equal to a + 42. In congruent triangles, corresponding sides are equal in length. Therefore: DE = EF Since FG is the sum of DG and EG, and EG is equal to DE (because DE = EF and EF = EG by congruency), you can express FG as: FG = DG + EG Given: DG = 3a EG = DE = EF (Because of the congruency between ΔDEG and ΔEFG) Since DE is congruent to EF, that implies EG = EF. So using the information that FG = DG + EG, we can substitute the given values into the equation: FG = 3a + EF We were also given that FG = a + 42. This allows us to set up the following equation since they both represent FG: 3a + EF = a + 42 However, to find FG, we do not actually need to solve for a or EF individually since FG equals a + 42 by the given information. Therefore: FG = a + 42 This is the expression for FG, and without additional information or numerical values provided for a, this is as simplified as it gets.
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