Question

Given: AC and BD are parallel. BX and CY are parallel. AX = DY. Prove: AYC is congruent to DXB

Answer 1

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Using the ASA congruency the triangles are congruent.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

For the two of the given triangles ΔACY and ΔDXB,

• ∠A = ∠D {Alternate Interior Angles}
• ∠DXB = ∠ACY {Alternate Interior Angles}
• AY = YD ⇒ (AX + XY) = (DY + XY) {Given AX=DY}

Since the measure of the two angles and one side of the two triangles are equal, therefore, using the ASA congruency the triangles are congruent.

Learn more about Triangle:

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