Question 1117254: a. Determine whether group A or group B (or both) show a pair of similar triangles or not. Tell how you know this.
b. For the group(s) with similar triangles, calculate all unknown side lengths. If possible, calculate the unknown angles. Explain your answers.
c. For the group(s) with similar triangles, calculate the scale factor. What is the relationship of the area of the original figure to the area of the translated figure? Explain.
d. For the group(s) with similar triangles, tell (roughly) what transformations would be needed to make one of the triangles carry onto the other triangle in its group.
picture:https://api.agilixbuzz.com/Resz/~zd4LEAAAAAAu0Z3cL67hsA.jTNXSlCDyD1Jr1Jk6_Dd0B/48780742,5CA,0,0/Assets/Media/Images/41.7-HOT1-Similarity.jpg
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
a. (are the pairs of triangles similar?)
The two triangles in group A are similar, because two angles of one are congruent to two angles of the other.
Note, however, that a purist would say the given information is inconsistent, because the 29.15 length shown for one side of the second triangle is only an approximation.
The two triangles in group B are not similar. The ratio of the short sides of the two triangles is 10:4 or 2.5:1; and that is the same ratio as the two sides 24 and 9.6. However, using the fact that an angle bisector in a triangle divides the opposite side into two segments in the same ratio as the lengths of the two sides that include the angle, the length of the third side of the left triangle can be found to be about 25.12; and 9.25 times 2.5 is not close to 25.12.
b. In group A, the third side of the first triangle, by the Pythagorean Theorem, is sqrt(306).
The scale factor between the two triangles is 3:5, so the length of the third side of the second triangle is 15*(5/3) = 25.
In both triangles the third angle measure is 31 degrees, since the sum of the three angles is 180.
c. The scale factor, again, is 3:5. That means the ratio of the areas of the two triangles is 3^2:5^2, or 9:25.
d. The first triangle can be carried onto the second with the following transformations:
(1) dilate by a factor of 5/3 to make it the same size;
(2) rotate 90 degrees counterclockwise;
(3) translate so the hypotenuses of the two triangles are the same line segment; and
(4) reflect about the hypotenuse
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