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90 POINTS- Please help with this geometry question! I have the answer because I assumed it was congruent, but I don't have the statement reasons.

90 POINTS- Please help with this geometry question! I have the answer because I assumed-example-1
User Rafols
by
7.9k points

1 Answer

4 votes

Answer:

A Δ DOC = 6 in²

Explanation:

Look at the attached graph

∵ ABCD is a trapezoid with legs AB and CD

AD // BC

In Δs ABC and DCB

BC is a common base

→ The heights of the Δs drawn from the points A and D to the base

BC are equal because the line joining A and D, AD is parallel to

the base BC

∴ Their heights are equal

→ Triangles of the same base and equal heights are equal in areas

A Δ ABC = A Δ DCB

∵ A Δ ABC = A Δ ABO + A Δ BOC

∵ A Δ DCB = A Δ DOC + A Δ COB

→ Equate their right sides

∴ A Δ ABO + A Δ BOC = A Δ DOC + A Δ COB

∵ A Δ BOC = A Δ COB ⇒ common triangle

∴ A Δ ABO = A Δ DOC

∵ A Δ ABO = 6 in²

A Δ DOC = 6 in²

90 POINTS- Please help with this geometry question! I have the answer because I assumed-example-1
User Hhbilly
by
8.5k points

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