Through point C, does not belong to two parallel planes and, two rays are drawn, one of which intersects

| February 8, 2021 | education

Through point C, does not belong to two parallel planes and, two rays are drawn, one of which intersects the planes and at points A1 and B1, respectively, and the second, respectively, at points A2 and B2. It is known that CA1 = 4 cm, B1B2 = 9 cm, A1A2 = CB1. Find A1A2 and A1B1.

The plane α is parallel to the plane β, then the segment A1B1 is parallel to A2B2. Consider two triangles CA2B2 and CA1B1. The angle C of the triangles is common, and the angles CA1B1 and CA2B2, CB1A1 and CB2A2 are also equal in pairs as the corresponding angles at the intersection of parallel straight lines.

Then triangles CA2B2 and CA1B1 are similar in three angles.

Let A1A2 be equal to X cm, then CB1 = X cm.Then CA2 = CA1 + A1A2 = 4 + X, CB2 = CB1 + B1B2 = X + 9.

CA2 / CA1 = CB2 / CB1.

(X + 4) / 4 = (X + 9) / X.

4 * X + 36 = X2 + 4 * X.

X2 = 36.

X = 6.

A1A2 = CB1 = 6 cm.

Answer: A1A2 = CB1 = 6 cm.



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