Similar Triangles Questions

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!


1)

Answer:


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



2)




Answer:


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

3)



Answer:


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

4)




Answer: x = 85°, y = 47°


5)




Answer:


Since CE / AB = CD / BC = 4/5 and ∠ABC = ∠ECD,


We can hence conclude that triangle BAC and triangle CED are similar (SAS)


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