Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Technical drawing wikipedia , lookup
Rational trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Multilateration wikipedia , lookup
Line (geometry) wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of geometry wikipedia , lookup
Geometry HS Mathematics Unit: 06 Lesson: 01 Properties of Quadrilaterals Properties of convex quadrilaterals: Have four sides. Have four vertices and angles. Sum of the angles equals 360o. Are congruent if their corresponding angles and corresponding sides are congruent. Quadrilaterals are generally classified by the number of parallel sides they contain. Study the definitions below. Trapezium – a quadrilateral with no pairs of parallel sides o Kite – two congruent pairs of adjacent sides Property Diagonals are perpendicular. One of the diagonals bisects the other. Trapezoid – a quadrilateral that has exactly one pair of parallel sides o Isosceles trapezoid – non parallel legs are congruent Property The base angles of an isosceles trapezoid are congruent. Parallelogram – a quadrilateral with two pair of parallel sides, opposite sides are parallel Properties Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Consecutive angles of a parallelogram are supplementary. The diagonals of a parallelogram bisect each other. o Rectangle – parallelogram with four right angles Property The diagonals of a rectangle are congruent. o Rhombus – parallelogram with four congruent sides Property The diagonals of a rhombus are perpendicular to each other. o Square – parallelogram with four right angles and four congruent sides Practice Problems 1. Write a proof for the statement, “Consecutive angles of a parallelogram are supplementary.” ©2012, TESCCC 04/25/13 page 1 of 4 Geometry HS Mathematics Unit: 06 Lesson: 01 Properties of Quadrilaterals 2. Write a proof for the statement, “The diagonals of a rhombus are perpendicular.” R H B M O 3. In the parallelogram below, BC = 2x – 7, AD = x + 5, and AC = 2x – 5. Find the value of x, BC, AD, and AC. B C A D 4. In the rectangle below, LK = 3 and LM = 4. Find KN, MN, KM, LN, LJ, MJ, KJ, and NJ. L M J K ©2012, TESCCC N 04/25/13 page 2 of 4 Geometry HS Mathematics Unit: 06 Lesson: 01 Properties of Quadrilaterals 5. How can a builder verify that each corner of a rectangular room forms a right angle without measuring the angles? 6. A rug is being woven in the shape of a rhombus so that one diagonal is 6 ft. long and the other is 8 ft. long. Fringe is to be place along the perimeter of the rhombus. How much fringe will be needed to edge the rhombus? 7. Use the trapezoid below to determine the value of x, the value of y, mF, mG, and mE. F G (12x+60)º (5y)º (4x+40)º 80º E H 8. Use the trapezoid below to determine XW, YZ, mWXY, mWZY, and mXYZ. X Y 60º W ©2012, TESCCC Z 04/25/13 page 3 of 4 Geometry HS Mathematics Unit: 06 Lesson: 01 Properties of Quadrilaterals 9. What is the perimeter of the kite, if TV = 10 feet? Round answer to the nearest tenth. U 45º 45º V T 60º 30º W ©2012, TESCCC 04/25/13 page 4 of 4