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| Congruent line segments: |
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| Definition |
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Line segments having the same length.
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- A line segment is denoted using capital letters at both ends.
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| Example |
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We can see that both line segments, \(PQ\) and \(RS\), have the same length.
Thus, \(PQ\) and \(RS\) are congruent.
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| Congruent angles: |
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| Definition |
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Angles having the same size.
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| Example |
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We can see that,
\(\angle PQR=40^\circ\) or \(\angle RQP=40^\circ\).
Thus, \(\angle PQR\) and \(\angle RQP\) are congruent.
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| Estimate and measure the length of a line segment and the size of an angle: |
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- An angle that appears more than a right angle has an angle greater than \(90^\circ\).
- An angle that appears less than a right angle has an angle less than \(90^\circ\).
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- The size of an angle can be measured more accurately using a protractor.
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| The properties of the angle on a straight line, a reflex angle and the angle of one whole turn: |
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The angle on a straight line
- The sum of angles on a straight line is \(180^{\circ}\).
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Reflex angle
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The angle of one whole turn
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| The properties of complementary angles, supplementary angles and conjugate angles: |
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Complementary angles
- The sum of the two angles is always \(90^\circ\).
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Supplementary angles
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Conjugate angles
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| Perform a geometrical construction: |
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(i) Line segments
- A section of a straight line with a fixed length.
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| Example |
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Construct the line segment \(AB\) with a length of \(8\text{ cm}\) using only a pair of compasses and a ruler.
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(ii) Perpendicular bisectors
- If line \(AB\) is perpendicular to line segment \(CD\) and divide \(CD\) into two parts of equal length, then line \(AB\) is known as the perpendicular bisector of \(CD\).
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| Example |
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Construct the perpendicular bisector of line segment \(PQ\) using only a pair of compasses and a ruler.
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(iii) Perpendicular line to straight line
- If a line is perpendicular to line \(PQ\), then the line is known as perpendicular line to line \(PQ\).
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| Example |
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Using only a pair of compasses and a ruler, construct the perpendicular line from point \(M\) to the straight line \(PQ\).
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(iv) Parallel lines
- Lines that will never meet even when they are extended.
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| Example |
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Using only a pair of compasses and a ruler, construct the line that is parallel to \(PQ\) passing through point \(R\).
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| Construct angles and angle bisectors: |
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| (i) Constructing an angle of \(60^{\circ}\) |
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| Example |
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Using only a pair of compasses and a ruler, construct line \(PQ\) so that \(\angle PQR=60^\circ\).
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(ii) Angle Bisectors
- A line divides an angle into two equal angles.
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| Example |
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Using only a pair of compasses and a ruler, construct the angle bisector of \(\angle PQR\).
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