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Magazine Problem 1
Set up and write a proof of each conjecture. Once you have completed the proofs, add the theorems to your list. Inscribed angles that intercept the same or congruent arcs are congruent. (Inscribed Angles Intercepting Arcs Theorem)
Problem 1
What is the difference between a postulate and a theorem?
Problem 2
Set up and write a proof of each conjecture. Once you have completed the proofs, add the theorems to your list. The opposite angles of an inscribed quadrilateral are supplementary. (Cyclic Quadrilateral Theorem)
Problem 2
Write a two-column proof or a flowchart proof of the conjecture. Once you have completed the proofs, add the theorems to your list. If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. (Opposite Sides Parallel and Congruent Theorem)
Problem 7
Write a two-column proof or a flowchart proof of the conjecture. Once you have completed the proofs, add the theorems to your list. The diagonals of a rectangle are congruent. (Rectangle Diagonals Theorem)
Problem 7
Write a proof of the conjecture. Once you have completed the proofs, add the theorems to your list. As always, you may use theorems that have been proved in previous exercises in your proofs. The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments on the hypotenuse. (Altitude to the Hypotenuse Theorem)
Problem 9
Write a two-column proof or a flowchart proof of the conjecture. Once you have completed the proofs, add the theorems to your list. The base angles of an isosceles trapezoid are congruent. (Isosceles Trapezoid Theorem)
Problem 9
Write a proof of the conjecture. Once you have completed the proofs, add the theorems to your list. The sum of the measures of the four angles of a quadrilateral is \(360^{\circ} .\) (Quadrilateral Sum Theorem)
Problem 11
Write a two-column proof or a flowchart proof of the conjecture. Once you have completed the proofs, add the theorems to your list. If a diagonal of a parallelogram bisects two opposite angles, then the parallelogram is a rhombus. (Converse of the Rhombus Angles Theorem)
Problem 12
Write a proof of the conjecture. Once you have completed the proofs, add the theorems to your list. In an isosceles triangle, the altitudes to the congruent sides are congruent. (Altitudes to the Congruent Sides Theorem)
