Question

Prove Theorem 6-4.

Given: m AB = m CD in circle p
Prove m<1 = m<2
SEE PICTURE

Answer 1

Explanation:

m∠1 = m∠2 : Substitution AB=CD : Given

m<1=mAB,m<2=mCD: Measure of the central angle equals the measure of the arc

m∠1 = m∠2 : Substitution

Answer 2

Hence Proved m∠1 = m∠2.

Explanation:

We need to Prove m∠1 = m∠2

Solution:

Statement Reason

m arc AB = m arc CD Given

Now we know that by theorem;

"Central angle is always equal to arc subtended by it."

m∠1 = m arc AB, m∠2 = m arc CD Central angle (∠) = m arc

Now substituting the values in above step we get;

m∠1 = m∠2 Substitution

Hence Proved m∠1 = m∠2.