The sides of the parallelogram are 4.5 and 12, a bisector is drawn from the top of the acute angle, which divides the opposite side into two segments. Find the length of the largest of these segments.
1. Vertices of the parallelogram – A, B, C, D. AB = 4.5 units. BC = 12 units. AE – bisector (drawn to the BC side).
2. The bisector AE divides the parallelogram into two geometric shapes. One of them is the ABE triangle. According to the properties of the parallelogram, this triangle is isosceles. Therefore, AB = BE = 4.5 units.
3. Calculate the length of the segment CE:
CE = BC – BE = 12 – 4.5 = 7.5 units.
Answer: CE = 7.5 units of measure – the largest of the segments.
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