Mathematics
State which pairs of triangles are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :
Triangles
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Answer
In Δ DEF,
∠D = 70°, ∠E = 80°
⇒ ∠D + ∠E + ∠F = 180° [By angle sum property of triangle]
⇒ 70° + 80° + ∠F = 180°
⇒ ∠F + 150° = 180°
⇒ ∠F = 180° - 150°
⇒ ∠F = 30°
In Δ PQR
∠Q = 80° , ∠R = 30°
⇒ ∠Q + ∠R + ∠P = 180° [By angle sum property pf triangle]
⇒ 80° + 30° + ∠P = 180°
⇒ ∠P + 110° = 180°
⇒ ∠P = 180° - 110°
⇒ ∠P = 70°.
In Δ DEF and Δ PQR,
⇒ ∠D = ∠P = 70°
⇒ ∠E = ∠Q = 80°
⇒ ∠F = ∠R = 30°
Hence, Δ DEF ~ Δ PQR by A.A.A. axiom.
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