The bisectors of the parallelogram angles adjacent to the larger side divide the opposite side into three parts.

| April 25, 2021 | education

The bisectors of the parallelogram angles adjacent to the larger side divide the opposite side into three parts. Find these parts, bearing in mind that the sides of the parallelogram are 5 inches and 12 inches.

<BAD = 2 * <BAM (AM – bisector).
<BAD = <BCD (opposite angles of a parallelogram).
<BCD = 2 * <BAM;
<ABC = 180 ° – <BCD = 180 ° – 2 * <BAM;
<BMA = 180 ° – <BAM – <ABC =
= 180 ° – <BAM – (180 ° – 2 * <BAM) = <BAM.
ΔABM – isosceles.
BM = AB = 5 dm.

<ADC = 2 * <NDC (DN – bisector).
<ADC = <ABC (opposite angles of a parallelogram).
<ABC = 2 * <NDC;
<BCD = 180 ° – <ABC = 180 ° – 2 * <NDC;
<DNC = 180 ° – <NDC – <BCD =
= 180 ° – <NDC – (180 ° – 2 * <NDC) = <NDC.
ΔNCD is isosceles.
NC = CD = 5 dm.

MN = BC – BM – NC = 12 – 5 – 5 = 2 dm.

Answer: 5 dm, 2 dm, 5 dm.



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