Question

!!50 point!!!

for each statement determine if "yes it is possible to decomposition" or "no it is not possible to decomposition" and explain your reasoning

statement A: the area of triangle GHL plus the area of triangle HIJ

statement B: the area of the triangle GHK plus the area of triangle HIK

statement C: the area of the triangle GJK plus the area of triangle ILK

statement D: the area of triangle GHK plus the area of triangle ILK ​

Answer 1

• B: the area of the triangle GHK plus the area of triangle HIK

Explanation:

Connect points H and K and you have two triangles:

• ΔGHK and ΔHIK

The answer options:

statement A:

• the area of triangle GHL plus the area of triangle HIJ
• False. This leaves a gap (HJKL)

statement B:

• the area of the triangle GHK plus the area of triangle HIK
• True

statement C:

• the area of the triangle GJK plus the area of triangle ILK
• False. This leaves a gap and overlap.

statement D:

• the area of triangle GHK plus the area of triangle ILK ​
• False. This leaves a gap and overlap.