If ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣=∣∣
∣∣a1b11a2b21a3b31∣∣
∣∣ then the two triangles with vertices (x1,y1),(x2,y2)(x3,y3)and(a1,b1),(a2,b2),(a3,b3) must be congruent . Is this true ?
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Solution
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If Δ1andΔ2 be the areas of the two triangles , then the given equality implies 2Δ1=2Δ2 Areas are equal and this does not necessarily implies that they are congruent as well.
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Q1
If ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣=∣∣
∣∣a1b11a2b21a3b31∣∣
∣∣ then the two triangles with vertices (x1,y1),(x2,y2)(x3,y3)and(a1,b1),(a2,b2),(a3,b3) must be congruent . Is this true ?
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Q2
If ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣=∣∣
∣∣a1b11a2b21a3b31∣∣
∣∣, then the two triangles with vertices (x1,y1),(x2,y2),(x3,y3) and (a1,b1), (a2,b2), (a3,b3) must be congruent.
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Q3
If ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣=∣∣
∣∣a1b11a2b21a3b31∣∣
∣∣ then the two triangles with vertices (x1,y1),(x2,y2),(x3,y3) and (a1,b1),(a2,b2),(a3,b3) are
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Q4
If ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣ = ∣∣
∣∣111b1b2b3a1a2a3∣∣
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Q5
If ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣=∣∣
∣∣111b1b2b3a1a2a3∣∣
∣∣ then the two triangles whose vertices are (x1,y1),(x2,y2),((x3,y3) and (a1,b1),(a2,b2),(a13,b3), are