If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true
a. EF/PR = DF/PQ
b. DE/PQ = EF/RP
c. DE/QR = DF/PQ
d. EF/RP = DE/QR
Solution:
Given, the two triangles DEF and PQR.
Also, ∠D = ∠Q and ∠R = ∠E
We have to find the true statement from the options.
As ∠D = ∠Q and ∠R = ∠E
It is clear that the corresponding angles are equal. So, the third angle will also be equal.
AAA criterion states that if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.
By AAA criterion,
The triangles DEF and PQR are similar.
The corresponding sides will be
DF/PQ = DE/QR = EF/PR
Taking DF/PQ = DE/QR
Therefore, option C is true.
Taking DE/QR = EF/PR
Therefore, option D is true
Taking DF/PQ = EF/PR
Therefore, option A is true.
✦ Try This: If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E, then which of the following statements is false?
a. EF/PR = DE/PQ
b. DE/PQ = EF/RP
c. DE/QR = DF/PQ
d. EF/RP = DE/QR
Given, in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E
We have to find the false statement from the options.
AAA criterion states that if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.
As ∠D ≅ ∠Q and ∠R ≅ ∠E
The third angle will also be equal.
The triangles DEF and PQR are similar.
So, the corresponding sides will be
DE/QR = DF/QP = EF/RP
From the options, DE/PQ = EF/RP is false
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.1 Problem 6
If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true, a. EF/PR = DF/PQ, b. DE/PQ = EF/RP, c. DE/QR = DF/PQ, d. EF/RP = DE/QR
Summary:
If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then b. DE/PQ = EF/RP is false
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