The segments KE and MN intersect at point O, so the KM segment is parallel to the NE segment:
August 24, 2021 | education
| The segments KE and MN intersect at point O, so the KM segment is parallel to the NE segment: a) prove that KO ON = MO OE; b) find KM if MN = 20cm, MO = 12cm, NE = 18cm.
Since the lines KM and NE are parallel, and the lines MN and KE are secant at these lines, then
<ONE = <OMK; <OEN = <OKM as criss-cross corners.
<NOE = <KOM – vertical angles.
Three angles of one triangle are equal to three angles of another triangle, which means triangles
OKM and OEN are similar.
Therefore, we can write down the proportion:
KO: OE = MO: ON = KM: NE; that is: KO * ON = OE * MO;
KM * ON = NE * MO;
ON = MN – MO = 20 – 12 = 8 (cm);
KM = NE * MO: ON = 18 * 12: 8 = 27 (cm).
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