Answer:
<u>Congruent pairs of triangles:</u>
ΔABD ≅ ΔDCB
- AB≅CD - given
- ∠ABD ≅ ∠CDB - given
- BD≅DB - common side
- SAS - two sides and the included angle
ΔABD ≅ ΔEFD - SAS
- AB≅EF - given
- ∠ABD ≅ ∠EFD - given
- ∠ADB ≅ ∠EDF - vertical angles
- AAS - two angles and non-included side
<u>By using the above two we can state that:</u>
ΔBDC ≅ ΔDFE - by ASA or SSS
because
- BD ≅ DF (corresponding parts)
- AD ≅ BC (corresponding parts)
- AD ≅ ED (corresponding parts)
- and therefore BC ≅ ED
<u>We can't prove that:</u>
- ΔAGD is congruent with any of the others as not enough information
There is one side and one angle and we can' t get two angles or two sides with included angle. Maximum we can get is SSA which doesn't guarantee the congruence.
Answer: 18 baskets
Explanation:
Let n = number of baskets that can be filled so that the baskets are identical and there are no eggs left over
Each color of eggs divisible by n must be equal to each other
18 green eggs, 36 red eggs and 54 blue eggs
18/n = 36/n = 54/n
Using logic and plug in method
All of them are divisible by 2, 3, 6, 9 and 18
The greatest is 18.
18 is therefore the greatest number of baskets that you can fill so that the baskets are identical and there are no eggs left over.
Another method is to use HCF among the 18 green eggs, 36 red eggs and 54 blue eggs.
This means that each basket will contain 1 green egg, 2 red eggs and 3 blue eggs.
