Updated: Jun 22, 2021
Hi students of Math Lobby! We believe you have completed reading the article regarding the similarity of triangles before clicking into this article and the following questions are for you to practice and strengthen your understanding on the topic of similar triangles. However, if you haven’t, then be sure to check it out first to get your fundamentals straight before proceeding with these questions! You can head to the article on similar triangles right here!
Without further ado, let’s begin!
Since ∠ABC = ∠AB’C’ and ∠ACB = ∠AC’B’,
We can conclude that triangle ABC is similar to triangle AB’C’ (AA)
To find the length of AC,
B’C’ / BC = 5 / 10 = 1/ 2
Therefore, (AC – 3) / AC = 1 / 2
2AC – 6 = AC
AC = 6cm
Since ∠ACB = ∠A’C’B’ and ∠BAC = ∠B’A’C’,
We can conclude that triangle ABC is similar to triangle A’B’C’ (AA).
To find the length of B’C,
A’B’ / AB = B’C’ / BC = 9 / 15
9 / 15 = (3 + B’C) / (8 + B’C)
72 + 9 B’C = 45 + 15 B’C
6 B’C = 27
Therefore, B’C = 4.5cm
Since ∠AEB = ∠CEF and ∠DBE = ∠CBF,
We can conclude that triangle ABE is similar to triangle CFE (AA), and triangle DBE is similar to triangle CBF (AA)
To find the length of CF,
Let BF be x and BE be y,
CF / 12 = (y-x) / y CF / 18 = x / y
CF / 12 = 1 – (x/y)
Hence, CF / 12 = 1 – (CF/18)
(CF/12) + (CF/18) = 1
CF = 36/5 = 7.2cm
Answer: x = 85°, y = 47°
Since CE / AB = CD / BC = 4/5 and ∠ABC = ∠ECD,
We can hence conclude that triangle BAC and triangle CED are similar (SAS)
Since triangles BAC and CED are similar,
∠CDE = ∠BCA = 70°
Hence, ∠BAC = 180° - 60° - 70° = 50°
· ∠ACB is not equal to ∠DCE since line AE wasn’t stated to be a straight line (Opposite angles rule does not apply!)
· ∠BDE is not equal to ∠ABE since line AB and line DE are not parallel.
And that’s all for today, students! We believe that these questions are good enough to keep those brain juices flowing and the practice has strengthened your foundation and understanding of this chapter on similar triangles! If you have any pending questions, please do go on to our Facebook page, Instagram or contact us directly at Math Lobby! Our math tutors will aid you in your journey to becoming a better student!
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