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Answers
1....1. the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
example. (1, -3) and B(4, 5).
2.
i.A part of a line with a start point but no end point (it goes to infinity) Try moving points "A" and "B": line.
ii. A line is named by any two points on it and written as line AB or line PQ. One and only one line can be drawn passing through two given points A and B. This line is called AB.
1.4.
ii. If all sides of a triangle are congruent, then its all angles are congruent.
Antecedent (Given): All the sides of the triangle
are congruent.
Consequent (To prove): All the angles are congruent.
i. The diagonals of a parallelogram bisect each other. Conditional statement: "If a quadrilateral is a parallelogram then its diagonals bisect each
other.
Antecedent (Given): Quadrilateral is a parallelogram.
Consequent (To prove): Its diagonals bisect each other
5.i. attachment is give
Explanation:
2.3.
Proof : If two lines intersect each other, then the vertically opposite angles are equal.
In the statement above, it is given that ‘two lines intersect each other’. So, let AB and CD be two lines intersecting at O (as shown in Fig. show attachment) They lead to two pairs of vertically opposite angles, namely,
(i) ∠ AOC and ∠ BOD (ii) ∠ AOD and ∠ BOC.
We need to prove that ∠ AOC = ∠ BOD and ∠ AOD = ∠ BOC.
Now, ray OA stands on line CD.
Therefore, ∠ AOC + ∠ AOD = 180° (Linear pair axiom) ………..(1)
Can we write ∠ AOD + ∠ BOD = 180°? (Linear pair axiom)……………(2)
From (1) and (2), we can write
∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD
This implies that ∠ AOC = ∠ BOD
Similarly, it can be proved that ∠AOD = ∠BOC
2.4.i . attachment is given 4.i
2.5.
i. Ray PQ
ii. Ray QR
iii. point s
Answer:
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