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3. A) Point-Line-Plane Theorem (Postulate)

4.B) Linear Pair Theorem

5.C)Vertically Opposite Angle Theorem

Step-by-step explanation:

3. The Point-Line-Plane Theorem(Postulate) states that if a line is drawn between two points, then the line and another non-collinear point (a point that doesn't lie on the line) share the same plane. Hence, the line and the point, assuming that its not on the line, are coplanar.

4.We know that an angle around point on a straight line is 180 degree.  Hence, the Linear Pair Theorem tells us that if generally two angles are on a straight line (Linear), the two angles are supplementary. Hence, as Angles 1 and 2 lie on the same line, the sum of the measures of both angles is 180 degree or they are supplementary.

5. The Vertical Angles Theorem states that if two lines intersect, then the vertically opposite angles formed between the lines, stand equal or congruent. Here, as Angle 2 and Angle 4 are vertically opposite to each other, they are equal(congruent) too.

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step-by-step explanation:

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