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  • 36Steps
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In this program, you will: 1. Accept results established in earlier grades as axioms that a tangent to a circle is perpendicular to the radius drawn to the point of contact 2. Then investigate and prove the theorems of the geometry of circles and use the theorems and their converses, where they exist, to solve riders 3. Revise earlier work on the necessary and sufficient conditions for polygons to be similar 4. Prove (accepting results established in earlier grades): • That a line drawn parallel to one side of a triangle divides the other two sides proportionally (and the Mid-point Theorem as a special case of the converse of this theorem) • That equiangular triangles are similar • That triangles with sides in proportion are similar • The Pythagorean Theorem by similar triangles

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