Question

Geometry
Q1. Proof the opposite angles formed by 2 intersecting lines are of equal measures
Q2. Coordinates of some pairs are given below. Hence find the distance between each pair
a. y+2, y-2 b.31, -42
Q3. On a number line, points X, Y and Z are such that d( X,Z) = 11.5,d(Z,Y)= 7.5. Find d (X,Y) considering all possibilities.
Q4. Write the following statement in conditional form and also its Converse statement​

Answer 1

Answer:

 : If two lines intersect each other, then the vertically opposite angles are equal.

Proof :



In the statement above, it is given that ‘two lines intersect each other’. So, let AB and CD be two lines intersecting at O as shown in Fig. 6.8. They lead to two pairs of vertically opposite angles, namely,

(i) ∠ AOC and ∠ BOD (ii) ∠ AOD and ∠ BOC.

 

We need to prove that ∠ AOC = ∠ BOD and ∠ AOD = ∠ BOC.

Now, ray OA stands on line CD.

Therefore, ∠ AOC + ∠ AOD = 180°  (Linear pair axiom) ………..(1)

Can we write ∠ AOD + ∠ BOD = 180°?  (Linear pair axiom)……………(2)

From (1) and (2), we can write

∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD

This implies that ∠ AOC = ∠ BOD

Similarly, it can be proved that ∠AOD = ∠BOC