22A Core skills 1. Match the word on the left below with its defi nition on the right and rewrite them in your copybook. Word
Defi nition
Theorem Converse Axiom
Corollary Proof
Implies Have the exact same shape and size
Statement that follows from a previous theorem Step-by-step explanation using axioms and theorems Used when a fact is proven by previous statements A statement taken to be true without proof
Statement from axioms and theorems by logical argument Congruent triangles The reverse of a theorem
2. Show that the following pairs of triangles are congruent. Explain why they are congruent in each case. (i)
B (ii) I W C (iii) G T J R A
A (iv) B
C S
R T
B (v) F
A S
N A
G (vi) J
H T
E A
C
A
D
D
E
N
K
L
3. Calculate the length of the missing side in each of the following right-angled triangles. ? cm
(i) 28 cm 45 cm
4. Use Pythagoras’s theorem to fi nd the length of the unknown side in each of the following shapes. G
(i) 9 E ? F K H 15 8 8 N 6 (ii) M ? L (iii)
A ? 5
5. Investigate the following triangles to determine if they are right-angled or not. (i)
(ii) 3 cm 5 cm 5.8 cm 4.5 cm 7 cm 8 cm D 4 Z B V C (iv) U ? Y
6. Ethna makes a rectangular sandwich that is 12 cm long and 5 cm wide. If she cuts it in half diagonally, what is the length of the cut edge?