Complete each statement. A tangent is ___ to the radius drawn to the point of tangency.

Write a proof of the conjecture. Once you have completed the proofs, add the theorems to your list. If a line passes through two sides of a triangle parallel to the third side, then it divides the two sides proportionally. (Parallel/Proportionality Theorem)

Write a coordinate proof of each conjecture. If it cannot be proven, write "cannot be proven." The quadrilateral formed by connecting the midpoint of the base to the midpoint of each leg in an isosceles triangle is a rhombus.

Is the proof in the earlier example claiming that if one diagonal of a quadrilateral bisects the other, then the quadrilateral is not a trapezoid? Explain.

For each statement, select always (A), sometimes (S), or never (N). a. An angle inscribed in a semicircle is a right angle. b. An angle inscribed in a major arc is obtuse. c. An arc measure equals the measure of its central angle. d. The measure of an angle formed by two intersecting chords equals the measure of its intercepted arc. e. The measure of the angle formed by two tangents to a circle equals the supplement of the central angle of the minor intercepted arc.

When you state AC=AC, what property are you using? When you state $\overline{A C} \cong \overline{A C}$, what property are you using?

If you need a perpendicular line in a proof, which postulate allows you to construct it?

Set up and write a proof of each conjecture. Once you have completed the proofs, add the theorems to your list. If a parallelogram is inscribed within a circle, then the parallelogram is a rectangle. (Parallelogram Inscribed in a Circle Theorem)

Find angle measures x and y, and length a.

Set up and write a proof of each conjecture. Once you have completed the proofs, add the theorems to your list. Parallel lines intercept congruent arcs on a circle. (Parallel Secants Congruent Arcs Theorem)

Write a coordinate proof of each conjecture. If it cannot be proven, write "cannot be proven." The figure formed by connecting the midpoints of the sides of a quadrilateral is a parallelogram.

Add the reflexive property of congruence, the transitive property of congruence, and the symmetric property of congruence to your notebook. Include a diagram for each property. Illustrate one property with congruent triangles, another property with congruent segments, and another property with congruent angles. (These properties may seem ridiculously obvious. This is exactly why they are accepted as premises, which require no proof!)

Devise a plan and write a proof of each conjecture. If two chords intersect in a circle, the product of the segment lengths on one chord is equal to the product of the segment lengths on the other chord.

Is the proof in the earlier example claiming that if two angles of a triangle are not congruent, then the triangle is not isosceles? Explain.