Question

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

Answer 1

Inscribed angles theorem

Explanation:

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Answer 2

See explanation

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:
`\angle A\cong \angle D`

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:

`\angle O=2\angle A...(1)`

`\angle O=2\angle D...(2)`

The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.

This implies that:

`2\angle A=2\angle D`

`\therefore \angle A\cong \angle D`