Question

In the
given figure
figure AB and CD interset do
Prove that AC=BD. it.
D​

Answer 1

Step-by-step explanation:

in triangle ACO and triangle BOD

AO = Bo (givenl

co = Do (given)

angle aoc equal angle bod (vertical opposite angle)

so triangle aco and triangle bod are congruent triangle

so by cpct rule

ac equal bd

hope this is helpful

thankyou

Answer 2

GiveN:-

In ∆AOC and ∆BOD,

• CO = OD
• AO = OB

To FinD:-

Prove that AC=BD.

SolutioN:-

• AO = OB (AB intersect at O)
• CO = OD (CD intersect at O)

So,

In ∆AOC and ∆BOD,

$\large\implies{\sf{AO=OB\:(\because\:AB\: intersect\:at\:O)}}$

$\large\implies{\sf{CO=OD\:(\because\:CD\: intersect\:at\:O)}}$

$\large\implies{\sf{\angle\:AOC=\angle\:BOD\:(\because{vertically\:opposite\:angles)}}}$

$\large\implies{\sf{\triangle{AOC}\cong\:\triangle{BOC}\:(By\:SAS\:congruency)}}$

$\large\implies{\sf{AC=BD\:(cpct)}}$

$\large\therefore\boxed{\bf{AC=BD(proved).}}$

Note:- "cpct" means corresponding parts of congruent triangle.

Explore More:-

• SSS congruency:-

Three sides of one triangle are equal to the three sides of another triangle.

• SAS congruency:-

Two sides and the included angle of one triangle are equal to the two sides and included angle of another triangle.

• ASA congruency:-

Two angles and the included side of one triangle are equal to the two angles and included side of another triangle.

• RHS congruency:-

The hypotenuse and a side of one right angled triangle are equal to the hypotenuse and a side of the right angled triangle.