Geometry: An Interactive Journey to Mastery

Study Tip
x This lesson is purely optional. There are no recommended study tips for this lesson other than to enjoy
the lesson and let the thinking about it strengthen your understanding of geometry as a whole.
Pitfall
x Don’t forget to have fun in your thinking of mathematics. This is a fun topic.

1. If every year you were given a birthday cake with as many candles as your new age, how many birthday
   candles have you blown out in your life?


2. The number 1225 is both square and triangular. It is the 35thVTXDUHQXPEHUͼ௘ZHKDYHSͼ௘௘ͽ ^2  ௘ͽ
   Which triangular number is it?


3. &RQVLGHUWKUHHFRQVHFXWLYHWULDQJXODUQXPEHUV8VHJHRPHWU\²RUSHUKDSVDOJHEUD²WRH[SODLQZK\VL[
   copies of the middle number combined with the other two is sure to give a square number.ͼ௘$VDQH[DPSOH
   WKHWKUHHWULDQJXODUQXPEHUVDQGJLYHî ZKLFKLVVTXDUH௘ͽ


4. If Sͼ௘N௘ͽGHQRWHVWKHNth square number, show that Sͼ௘N + M௘ͽ Sͼ௘N௘ͽSͼ௘M௘ͽMN.

Problems