Lesson 13.1 The Premises of Geometry

Transcription

1 Lesson 13.1 The remises of Geometry 1. rovide the missing property of equality or arithmetic as a reason for each step to solve the equation. Solve for x: 5(x 4) 2x 17 Solution: 5(x 4) 2x 17 a. 5x 20 2x 17 3x x 37 x b. c. d. e. In Exercises 2 4, identify each statement as true or false. If the statement is true, tell which definition, property, or postulate supports your answer. If the statement is false, give a counterexample. 2. If M M, then M is the midpoint of. 3. If is on and is not, then m m If ST and KL, then ST KL. 5. omplete the flowchart proof. Given:,, Flowchart roof Given ostulate 84 HTER 13 iscovering Geometry ractice Your Skills 2008 Key urriculum ress

2 Lesson 13.2 lanning a Geometry roof For these exercises, you may use theorems added to your theorem list through the end of Lesson In Exercises 1 3, write a paragraph proof or a flowchart proof for each situation. 1. Given:, 2. Given: ST, R STU R UT R T U S 3. Given: Noncongruent, nonparallel segments,, and x y z 180 x a b y c z iscovering Geometry ractice Your Skills HTER Key urriculum ress

3 Lesson 13.3 Triangle roofs Write a proof for each situation. You may use theorems added to your theorem list through the end of Lesson Given: XY ZY, XZ WY W 2. Given:,, WXY WZY X M Z Y 3. Given: MN M, NO M, 4. Given:, E, is the midpoint of MO R MN RON E O E N M 86 HTER 13 iscovering Geometry ractice Your Skills 2008 Key urriculum ress

4 Lesson 13.4 uadrilateral roofs In Exercises 1 6, write a proof of each conjecture on a separate piece of paper. You may use theorems added to your theorem list through the end of Lesson The diagonals of a parallelogram bisect each other. (arallelogram iagonals Theorem) 2. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. (onverse of the arallelogram iagonals Theorem) 3. The diagonals of a rhombus bisect each other and are perpendicular. (Rhombus iagonals Theorem) 4. If the diagonals of a quadrilateral bisect each other and are perpendicular, then the quadrilateral is a rhombus. (onverse of the Rhombus iagonals Theorem) 5. If the base angles on one base of a trapezoid are congruent, then the trapezoid is isosceles. (onverse of the Isosceles Trapezoid Theorem) 6. If the diagonals of a trapezoid are congruent, then the trapezoid is isosceles. (onverse of the Isosceles Trapezoid iagonals Theorem) In Exercises 7 9, decide if the statement is true or false. If it is true, prove it. If it is false, give a counterexample. 7. quadrilateral with one pair of parallel sides and one pair of congruent angles is a parallelogram. 8. quadrilateral with one pair of congruent opposite sides and one pair of parallel sides is a parallelogram. 9. quadrilateral with one pair of parallel sides and one pair of congruent opposite angles is a parallelogram. iscovering Geometry ractice Your Skills HTER Key urriculum ress

5 Lesson 13.5 Indirect roof 1. omplete the indirect proof of the conjecture: In a triangle the side opposite the larger of two angles has a greater measure. Given: roof: with m m ssume ase 1: If, then is by. y,, which contradicts. So,. ase 2: If, then it is possible to construct point on such that, by the Segment uplication ostulate. onstruct, by the Line ostulate. is. omplete the proof In Exercises 2 5, write an indirect proof of each conjecture. 2. Given:, 3. If two sides of a triangle are not congruent, then the angles opposite them are not congruent. 4. If two lines are parallel and a third line in the same plane intersects one of them, then it also intersects the other. 88 HTER 13 iscovering Geometry ractice Your Skills 2008 Key urriculum ress

6 Lesson 13.6 ircle roofs Write a proof for each conjecture or situation. You may use theorems added to your theorem list through the end of Lesson If two chords in a circle are congruent, then their arcs are congruent. 2. Given: Regular pentagon E inscribed in circle O, with diagonals and and trisect E E O 3. Given: Two circles externally tangent at R, common external tangent segment TS T S TRS is a right angle R 4. Given: Two circles internally tangent at T with chords T and T of the larger circle intersecting the smaller circle at and T iscovering Geometry ractice Your Skills HTER Key urriculum ress

7 Lesson 13.7 Similarity roofs Write a proof for each situation. You may use theorems added to your theorem list through the end of Lesson Given: with 2 2. The diagonals of a trapezoid divide each other into segments with lengths in the same ratio as the lengths of the bases. 3. In a right triangle the product of the lengths of the two legs equals the product of the lengths of the hypotenuse and the altitude to the hypotenuse. 4. If a quadrilateral has one pair of opposite right angles and one pair of opposite congruent sides, then the quadrilateral is a rectangle. 90 HTER 13 iscovering Geometry ractice Your Skills 2008 Key urriculum ress