4
Comparing segments
Textbook: pp. 12–13
GoalKnow equal figures, how to compare segments and the midpoint.
New words
equal (congruent) figures · teng shakllarlaying a segment on a ray · kesmani nurga qo‘yishmidpoint of a segment · kesmaning o‘rtasicoinciding · ustma-ust tushish
Explanation
If one figure can be moved so that it matches another completely, the two figures are called equal. Axiom: on any ray, starting from its origin, exactly one segment equal to a given segment can be laid off. To compare two segments, lay both on one ray starting at the same point: if they coincide the segments are equal; if one lies inside the other it is shorter. The midpoint of a segment is the point dividing it into two equal segments; if AC = CB, then C is the midpoint of AB. In drawings, equal segments are marked with the same number of small ticks.
Worked examples
If AB = 5 cm and CD = 8 cm are laid on one ray from the same point, CD extends beyond AB, so CD > AB.
If C is the midpoint of AB and AC = 7 cm, then CB = 7 cm and AB = 14 cm.
Class activity
“Tracing paper test”: copy a segment onto tracing paper and place it on other segments. Which pairs are equal? (Use scissors only with an adult’s help.)
Practice
1
C is the midpoint of AB, AB = 18 cm. Find AC (in cm).
9
2
If AC = CB, what is point C for segment AB?
The midpoint
3
Two segments are laid on a ray from the same point and one extends beyond the other. Which is longer?
The one that extends beyond is longer.
4
Why do we get a unique segment when laying a segment on a ray?
This is an axiom: on a ray there is only one segment from the origin equal to a given one.