isi-entrance 2024 Q3

isi-entrance · India · UGB Proof Direct Proof of a Stated Identity or Equality

Let $ABCD$ be a quadrilateral with all internal angles $< \pi$. Squares are drawn on each side as shown in the picture below. Let $\Delta _ { 1 } , \Delta _ { 2 } , \Delta _ { 3 }$ and $\Delta _ { 4 }$ denote the areas of the shaded triangles shown. Prove that
$$\Delta _ { 1 } - \Delta _ { 2 } + \Delta _ { 3 } - \Delta _ { 4 } = 0 .$$

Let $ABCD$ be a quadrilateral with all internal angles $< \pi$. Squares are drawn on each side as shown in the picture below. Let $\Delta _ { 1 } , \Delta _ { 2 } , \Delta _ { 3 }$ and $\Delta _ { 4 }$ denote the areas of the shaded triangles shown. Prove that

$$\Delta _ { 1 } - \Delta _ { 2 } + \Delta _ { 3 } - \Delta _ { 4 } = 0 .$$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8