* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 5 Review Handout File
Survey
Document related concepts
Technical drawing wikipedia , lookup
Riemannian connection on a surface wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
List of regular polytopes and compounds wikipedia , lookup
Complex polytope wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Rational trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Trigonometric functions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Line (geometry) wikipedia , lookup
History of geometry wikipedia , lookup
Transcript
Geometry - Chapter 5 Review – Polygon Properties Name ______________________________________ Date __________ Hour __________ Complete each statement by filling in the blank. 1. The sum of the measures of the n interior angles of an n-gon is ____________________. 2. For an equiangular n-gon, each interior angle can be found using the formula _____________. 3. For any polygon, the sum of the measures of a set of exterior angles is ______________. 4. The ________________ angles of a kite are congruent. 5. The diagonal connecting the vertex angles of a kite is the ______________________________ of the other diagonal. 6. The vertex angles of a kite are _________________ by a ______________________. 7. The consecutive angles between the bases of a trapezoid are ________________________. 8. The base angles of an isosceles trapezoid are ___________________. 9. A midsegment of a triangle is parallel to the third side and ________________ the length of the _______________________. 10. The midsegment of a trapezoid is parallel to the bases and is equal in length to the ________________ of the lengths of the ______________. 11. The opposite angles of a parallelogram are __________________. 12. The consecutive angles of a parallelogram are ___________________________. 13. The diagonals of a rhombus are _____________________ and they _______________ each other. 14. The diagonals of a rectangle are ___________________ and they _______________ each other. 15. The diagonals of a square are ______________, ____________________, and ___________ each other. 16. How many sides does a polygon have if the sum of its angle measures is 3240o? 17. How many sides does an equiangular polygon have if each interior angle measures 140o? 18. What is the measure of an exterior angle of an equiangular octagon? 1 Geometry - Chapter 5 Review – Polygon Properties 19. Find each lettered angle measure using your conjectures. a = ________ b = ________ c = ________ d = ________ e = ________ f = ________ g = ________ h = ________ 20. 21. s s = _____ m = _____ n = _____ p = _____ r = _____ s = _____ t = _____ t =_____ 22. Perimeter = 64 23. a x y 24. x = _____ y = _____ 25. x = _____ m = _____ a = _____ w = _____ x = _____ y = _____ 2 Geometry - Chapter 5 Review – Polygon Properties 26. 27. For the parallelogram below, find m and n. a = _____ b = _____ x = _____ y = _____ m = _____ 28. 29. n = _____ b c 7 cm a a = _____ b = _____ c = _____ d = _____ a = _____ b = _____ c = _____ 30. Complete the table below by placing a yes (to mean always) or a no (to mean not always) in each empty space. Kite Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Diagonals bisect each other Diagonals are perpendicular Diagonals are congruent Isosceles Trapezoid Parallelogram Rhombus Rectangle Square Yes Yes No No No 3 Geometry - Chapter 5 Review – Polygon Properties 31. A regular pentagonal mirror frame is to be built from strips of 2-inch-wide pine lattice. At what angles a and b should the lattice be cut? a = __________ b = __________ 32. A 2-inch-wide frame is to be built around the regular decagonal window shown. At what angles a and b should the corners of each piece be cut? a = __________ b = __________ 33. Prove that if the opposite sides of a quadrilateral are congruent, then it is a parallelogram. Hint: Draw KM . Given: Quadrilateral JKLM with JM KL and JK ML Show: JKLM is a parallelogram Quadrilateral JKLM with JM KL and JK ML JK LM CPCTC Converse of Parallel Lines Conj. Given Definition of Parallelogram Same segment 4 Geometry - Chapter 5 Review – Polygon Properties 34. Prove the conjecture: The diagonals of a rhombus bisect the angles. Given: Rhombus DENI, with diagonal DN Show: Diagonal DN bisects D and N Flowchart Proof DE ____ DENI is a rhombus _________ ___________________ 1 ______ 3 ______ ______ ______ NE ____ _______________ ________ ________ DN ____ _______________ DN bisects IDE and INE __________________ A 35. Prove the Parallelogram Opposite Sides Conjecture. Given: Parallelogram ABCD Show: AB CD and AD CB Complete the Flowchart Proof D 2 1 > > 4 3 B C AB | | CD Definition of parallelogram ________________ Parallelogram ABCD given _________________ _____________ ______________ _________________ _______________ 5