Consider a non-isosceles triangle △ABC.   Let: ℓ1 be the external angle bisector of ∠A, ℓ2 be the external angle bisector of ∠B and ℓ3 be the external angle bisector of ∠C. a) Explain why ℓ1‖̸BC, ℓ2‖̸AC and ℓ3‖̸AB. Also, Let ℓ1∩BC↔=D, ℓ2∩AC↔=E and ℓ3∩AB↔=F.  Prove that D, E and F are collinear.

Q: Draw and label right angle FGH  with a bisector    GI.

A: Given query is to Draw and label right angle FGH  with a bisector    GI.

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A: Consider triangle PQR, As RT bisect angle R, ∠PRT=∠QRT Given that ∠P=∠Q ∠RTP=∠1∠RTQ=∠2

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Q: State and prove the converse of the corresponding angles theorem.

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Q: (4) Prove that if two altitudes in a triangle are congruent, then the triangle is Isosceles.

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