Q1.
Observe Fig. 5.5 and describe the way the line segments meet or cross each other in each case, with appropriate mathematical words (a point, an endpoint, the midpoint, meet, intersect) and the degree measure of each angle. For example, line segments FG and FH meet at the endpoint F at an angle 115.3°.
Answer
There are five pairs in Fig. 5.5. Here is a description of each, with the angle you should get on measuring.
| Pair | How they meet | Angle |
|---|---|---|
| FG and FH | They meet at the endpoint F — F is an end of both segments (given example) | 115.3° |
| AB and CD | They intersect at a point X. X is inside both segments, so it is an endpoint of neither | about 60° (and 120° on the other side) |
| IJ and LM | They intersect at a point Y, which lies near the middle of each segment | about 79° (and 101° on the other side) |
| ST and UV | They do not meet at all inside the figure — no common point | no angle formed |
| OP and QR | They do not meet at all — they stay the same distance apart | no angle formed |
Why it happens: The words describe where the meeting happens. If the common point is an end of a segment we say the segments meet at an endpoint; if the common point lies inside both, we say the segments intersect at that point.
Tip: Measure all four angles at X and at Y. You should find two equal pairs each time, and each neighbouring pair adding to 180° — the very properties proved on page 107.