Measurements for Similar Triangles (1/2)
This video shows how to find measurements for similar triangles. For example, two pentagons are represented as such: ABCDE ~ FGHIJ. If the angles ABC, GHJ, BCD, HJK, DEA measure 120°, 100°, 100°, 120°, and 140°, respectively, what are the measures of the remaining angles? You need to use the Polygon Angle Sum Theorem, which states that n-2×180 is equal to the sum of the measures of the angles of any polygon. Doing this will tell you that every pentagon has 540°. Find the missing angle by adding the angles you have together and subtracting the total from 540.
Measurements for Similar Triangles Continued
Measurements for similar triangles. ABCDE is similar to, (that’s what that little squiggly line means), is similar to FGHJK. If the angle’s ABC, GHJ, BCD, HJK and DEA measure 120 degrees, 100 degrees, 100 degrees, 120 degrees, 140 degrees respectively, what are the measures of the remaining angles? We’re going to start by inserting this information in the problem onto the pictures.
Here we have are two similar Pentagons ABCDE and FGHJK. Angle ABC measures 120 degrees. Angle ABC is right here. That’s 120 degrees. Angle GHJ measures 100 degrees. GHJ, 100 degrees. Angle BCD measures 100 degrees. Angle HJK measurers 120. HJK, 120 degrees. Angle DEA measures 140 degrees. Now, since we were told that these figures are similar, similar figures have congruent corresponding angles.
All the angles and the shapes that are in the same places are congruent. That means since angle DEA measures 140 degrees that angle JKF measures 140 degrees. We could say the measure angle JKF equals 140 degrees. That’s one of the missing measures. Then on this Pentagon again, we have angle ABC as 120 which means angle FGH is 120 degrees. The measure of Angle FGH is 120 degrees.
On this Pentagon we have angle KJH is 120 degrees so the angle that corresponds to that in this figure would be angle EDC, so it’s also 120 degrees. The measure angle EDC is 120 degrees. We filled every angle that we can given the information that they’re similar and yet we still have two missing angles on both of our Pentagons.
We can find these missing angles by using the polygon angle sum theorem which says, N minus 2 times 180, is the sum of the measures of the angles of any polygon. We can find the total or the sum of the measures of the angles of this polygon. Since we’re only missing one angle then we can find that angle that’s missing. This polygon has five sides and the N stands for 5.
We substitute 5 for N. 5 minus 2, times 180. 5 minus 2 is 3. 3 times 180 Then 3 times 180 is 540. That means that all Pentagons have 540 degrees, or the of the measures of the angles is 540 degrees. We can find this missing angle here using Algebra. We know that if I add all five of these angles it will equal 540. I’ll start with this angle.120 Plus, 140 plus, 120 plus, 100, and I’m going to use an X for the angle we’re trying to find.
That’s one, two, three, four. That’s all five angles of our Pentagon and they should and to be 540 degrees. Now, we combine like terms. 100, 200, 300, 400, 440, 460, 480, so 480 plus X is equal to 540. Then to solve for X we need to subtract 480 from both sides. To find the measure of X. X is equal to 0 minus 0 is 0. We have to borrow from the 5 here.
That’s 14. 14 minus 8 is 6 and 4 minus 4 is 0. That means, that angle A measures 60 degrees. This is 60 so, angle EAB is 60 degrees. The measure of angle EAB is 60 degrees and the corresponding angle to that would be angle KFG. The measure of Angle KFG is also 60 degrees since the corresponding angles of similar figures are congruent. There are all the missing angle measures.