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raizagisselle1694
27.08.2019 •
Mathematics
How can i determine if polygons are similar
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Ответ:
This means: m ∠ A = m ∠ E, m ∠ B = m ∠ F, m ∠ C = m ∠ G, m ∠ D = m ∠ H, and It is possible for a polygon to have one of the above facts true without having the other fact true. The following two examples show how that is possible.In Figure 2, quadrilateral QRST is not similar to quadrilateral WXYZ.
Figure 2 Quadrilaterals that are not similar to one another.
Even though the ratios of corresponding sides are equal, corresponding angles are not equal (90° ≠ 120°, 90° ≠ 60°).In Figure 3, quadrilateral FGHI is not similar to quadrilateral JKLM.
Figure 3 Quadrilaterals that are not similar to one another.
Even though corresponding angles are equal, the ratios of each pair of corresponding sides are not equal (3/3≠5/3).Example 1: In Figure 4, quadrilateral ABCD ∼ quadrilateral EFGH. (a) Find m ∠ E. (b) Find x.
Figure 4 Similar quadrilaterals.
(a) m ∠ E = 90° (∠ E and ∠ A are corresponding angles of similar polygons, and corresponding angles of similar polygons are equal.)(b) 9/6 = 12/ x (If two polygons are similar, then the ratios of each pair of corresponding sides are equal.)
Ответ:
Add each given variable
(6x + 10) + (x + 2) + x = 8x + 12
The sum of all the angles equals 180ᴼ
8x + 12 = 180
Subtract 12 from both sides
8x = 168
Divide by 8 on both sides
x = 21
Now plug in 21 for each x to find the measure of each angle.
(6[21] + 10) = 126 + 10 = 136ᴼ
(21 + 2) = 23ᴼ
x = 21ᴼ