Q:

Two statements are missing reasons. What reasons can be used to justify both statements 2 and 3 ?

Accepted Solution

A:
Answer:See explanationStep-by-step explanation:The given circle has center O.A, B,C, and D are points on the circumference of the circle.We want to prove that: [tex]\angle A\cong \angle D[/tex]We need to join to B and C as shown in the attachment.Recall that angle subtended by arc BC at the center is twice the angle subtended at the circumference by the same arc.This implies that:[tex] \angle O=2\angle A...(1)[/tex][tex]\angle O=2\angle D...(2)[/tex]The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.This implies that:[tex]2\angle A=2\angle D[/tex][tex]\therefore \angle A\cong \angle D[/tex]