Question

Theorem : The opposite angles formed by two intersecting lines are of equal measures
Gen: Line AB and line CD intersect at point o such that A-O-B,C-O-D.
A
To prove: () ZAOC = ZBOD
(i) ZBOC = ZAOD
B
D
Fig. 1.15
Proof : ZAOC + ZBOC = 180° ....... (1) (angles in linear pair)
ZBOC + ZBOD = 180°
180° .......(ID)
(II) (angles in linear pair)
ZAOC + ZBOC = ZBOC + ZBOD ....... [from (1) and (IT)]
.. ZAOC = ZBOD.. eliminating ZBOC
Similarly, it can be proved that ZBOC = ZAOD.​

Answer 1

Answer:

Step-by-step explanation:

Gen: Line AB and line CD intersect at point o such that A-O-B,C-O-D.

A

To prove: () ZAOC = ZBOD

(i) ZBOC = ZAOD

B

D

Fig. 1.15

Proof : ZAOC + ZBOC = 180° ....... (1) (angles in linear pair)

ZBOC + ZBOD = 180°

180° .......(ID)

(II) (angles in linear pair)

ZAOC + ZBOC = ZBOC + ZBOD ....... [from (1) and (IT)]

.. ZAOC = ZBOD.. eliminating ZBOC

Similarly, it can be proved that ZBOC = ZAOD.​