Two towns that are 31.5 km apart are 3 cm apart on a map. what is the scale of the map?

1 cm : 10.5 km

Step-by-step explanation:

We are given that two towns are 31.5 km in real and are 3 cm apart on a map and we are to find the scale of the map.

For this, we can use the ratio method.

Therefore, the scale of the map would be 1 cm : 10.5 km.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.