Ahighway between points a and b has been closed for repairs. an alternative route between there two locations is to travel between a and c and then from c to b what is the value of y and what is the total distance from a to c to b?

The value of Y is 24 km and distance from A to C to B is AC+Y=18+24=42 km

Step-by-step explanation:

Given that A highway between points A and B has been closed for repairs. An alternative route between there two locations is to travel between A and C and then from C to B. we have to find the value of Y and the total distance from A to C to B. Let AB=Z

In ΔBCD and ΔABD

∠BCD=∠ABD       (∵each 90°)

∠D=∠D                 (∵common)

By AA similarity, ΔBCD~ΔABD

∴ their corresponding sides are proportional

Comparing last two terms, we get

⇒

⇒

⇒

⇒

⇒

Hence, the roots are X=32, -50

X=-50 not possible as distance can never negative.

Hence, X=32 km

By applying Pythagoras theorem in ΔBCD we get

⇒

⇒

Hence, the value of Y is 24 km and the distance from A to C to B is AC+Y=18+24=42 km

8

step-by-step explanation:

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.