Answer :
Answer:
Step-by-step explanation:
If, instead, one quarter were apples and one quarter were oranges and there were also 4 bananas, 3 pears, and 3 plums, how many would be apples?
Answer:
Step-by-step explanation:
To prove that the areas of triangles ADG and BEF are equal, we can follow these steps:
Identify congruent triangles:
Since CDH = CEH, triangles CDH and CEH are congruent.
Since DH = EH, triangles DHG and EHG are congruent.
Divide the given quadrilateral into triangles:
Quadrilateral ABDC can be divided into triangles ADG and BCF.
Quadrilateral ABCE can be divided into triangles BEF and ACF.
Establish congruent pairs of triangles:
Since AC = BC, triangles ACF and BCF are congruent.
Combine congruent triangles:
Combining congruent triangles ADG and DHG, we get triangle ADGH.
Combining congruent triangles BEF and EHG, we get triangle BEGH.
Compare areas of congruent triangles:
Since triangle ADGH is congruent to triangle BEGH, their areas are equal: A ADGH = A BEGH.
Combine congruent triangles:
Combining congruent triangles ACF and ADGH, we get triangle ACGH.
Combining congruent triangles BCF and BEGH, we get triangle BCEH.
Compare areas of congruent triangles:
Since triangle ACGH is congruent to triangle BCEH, their areas are equal: A ACGH = A BCEH.
Final conclusion:
From the previous steps, we have:
A ADGH = A BEGH
A ACGH = A BCEH
Adding these two equations, we get:
A ADGH + A ACGH = A BEGH + A BCEH
Since ACGH and BCEH overlap, their areas are subtracted twice in the above equation. Therefore, we can simplify it to:
A ADG = A BEF
Therefore, we have proven that the areas of triangles ADG and BEF are equal: A ADG = A BEF.
