Mathematics

Problem

A carpenter cuts two triangular wooden supports. Support 1 is right-angled

\triangle CAT

with right angle at

A

. Support 2 is right-angled

\triangle DOG

with right angle at

O

. He measures and finds

CT = DG = 15\ \text{cm}

and

CA = DO = 9\ \text{cm}

. a. (i) Prove that

\triangle CAT \cong \triangle DOG

. b. (ii) What can you say about the lengths

AT

and

OG

? Give a reason. c. (iii) If

AT

is found to be

12\ \text{cm}

, determine the length of

OG