In trapezoid ABCD, base BC = 12 cm, diagonal AC = 24 cm and angle BAC = angle ADC. Find the base AD.
| May 2, 2021 | education
1. ∠BAC = ∠ADC according to the problem statement.
2. ∠САD = ∠АСВ, since these angles are cross-lying, formed by the bases of the trapezoid BC and AD (parallel) and the diagonal AC intersecting them.
3. Therefore, triangle ABC is similar to triangle ACD (in two equal angles).
4. From the similarity of the indicated triangles it follows:
BC: AC = AC: AD.
AD = AC²: BC = 24 x 24: 12 = 48 centimeters.
Answer: The length of the AD base is 48 centimeters.
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