Are triangles formed in each figure similar? Ifso, name the criterion of similarity. Write the similarity relation in symbolic form.
Answers
Answer:
1.SAS
2.no
3SAS
4.SAS
5.AAA
6.AAA
7.no
8.no
Step-by-step explanation:
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i) Similar figure
ii) Not a Similar figure
iii) Similar figure
iv) Similar figure
v) Similar figure
vi) Similar figure
vii) Not a Similar figure
viii) Not a Similar figure
Given,
There are eight figures with different triangles
To find,
We must find the similarity, and their criteria, and write the similarity relation in symbolic form
Solution,
i) In ΔGHF and ΔIHK
GF = IK
∠H = ∠H
By Side-Angle-Side property,
GH = HI
Therefore, ΔGHF ~ ΔIHK
and they are similar triangles.
ii) In ΔPQR and ΔLMN
PQ ≠ LM
QR ≠ MN
∠Q = ∠M
Therefore, they are not similar triangles
iii) In ΔABC and ΔAXY
AB/AX = AC/AY
5/2 = 5/2
∠A = ∠A
By Side-Angle-Side property,
AY/AC = AY/AB
Therefore,
ΔAXY ~ ΔABC
They are similar triangles
iv) In ΔABC and ΔAPJ
AB/AP = AC/AJ
(5+3)/3 = (2 + (10/3))/2
8/3 = 8/3
By Side-Angle-Side property,
∠A = ∠A
ΔABC ~ ΔAPJ
They are similar triangles
v) In ΔAOQ and ΔPOB
∠A = ∠B
∠O = ∠O
By Angle-Angle-Angle property,
∠Q = ∠P
ΔAOQ ~ ΔPOB
They are similar triangles
vi) In ΔABC and ΔPQR,
∠A = ∠Q = 40°
∠B = ∠P = 60°
By Angle-Angle-Angle property,
∠C = ∠R = 80°
It is a similar triangle but not a corresponding triangle
vii) In ΔABC and ΔPQR,
AB/PQ = 2/5 = 0.4
BC/QR = 2
AC/PR = 2
It is not a similar triangle but not a corresponding triangle because the sides are not equal
viii) In ΔABC and ΔPQR,
∠A = ∠P
AB/PQ = 6/2.5 = 12/5
AC/PR = 2
They are not similar triangles but not corresponding triangles because the sides are not equal
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