Download 8.5 Properties of Trapezoids and Kites

Geometry Chapter 8: Quadrilaterals 8.5-­‐ Use Properties of Trapezoids and Kites SWBAT: use properties of trapezoids and kites. Common Core: G.CO.11, G.CO.13, G.SRT.5 “Do Now” Determine if the quadrilateral with given vertices is a parallelogram, rectangle, rhombus, or square. Show all work to support your answer and explain your conclusion. 𝑀 2, 2 , 𝐴 4, 3 , 𝑇 3, −1 , 𝐻(−3, −2) Parallelogram: __________ Rectangle: __________ Rhombus: __________ Square: __________ Explanation: A trapezoid is a quadrilateral with exactly one pair of _________________________ sides. The parallel sides are the _____________________. Label them in the diagram. ∠𝑇 and ∠𝑅 are a pair of ____________________ angles. Name another pair: The nonparallel sides are the ___________________ of the trapezoid. Label them in the diagram. ∠𝑇 and ∠𝑃 are ______________________________. Geometry Chapter 8: Quadrilaterals Isosceles Trapezoid: If the legs of a trapezoid are __________________________, then the trapezoid is an isosceles trapezoid. Label the trapezoid isosceles. A trapezoid is isosceles if and only each pair of base angles are ____________________________. Mark the base angles correctly in the diagram. A trapezoid is isosceles if and only if its ________________________ are congruent. If 𝐴𝐵𝐶𝐷 is an isosceles trapezoid, then ___________ ≅ ___________. Midsegment of a Trapezoid: The midsegment of a trapezoid is the segment that connects the ______________________________ of its legs. The midsegment of a trapezoid is _______________________ to each base and its length is the _______________________ of the two bases. 𝑀𝑁 ∥ __________, 𝑀𝑁 ∥ __________, 𝑀𝑁 = ______________________________. Geometry Chapter 8: Quadrilaterals Kite: A kite is a quadrilateral that has two pairs of consecutive ___________________________ sides, but the opposite sides are ____________________ congruent. If a quadrilateral is a kite, then exactly one pair of _________________________ angles are congruent. Label the diagram with congruent sides and angles. If a quadrilateral is a kite, then its __________________________ are perpendicular. If 𝑅𝑆𝑇𝑈 is a kite, then __________ ⊥ __________. Label the diagram so that is represents a kite. Practice: Find the missing value on the trapezoids below. 1. 2. Solve for x. 𝑚∠𝑊 = _____________ 𝑚∠𝑋 = _____________ Geometry Chapter 8: Quadrilaterals 3. 𝑚∠𝑄 = ____________ 4. 𝐷𝐸𝐹𝐺 is an isosceles trapezoid. 𝑚∠𝑅 = ____________ 𝐷𝐺 ≅ ____________ 𝑚∠𝑆 = ____________ 𝐷𝐹 ≅ ____________ 6. 5. Find 𝑚∠𝑅. 𝑚∠𝑊 = ____________ 𝑚∠𝑌 = ____________ 𝑚∠𝑍 = ____________ 7. If 𝑀𝑁𝑂𝑃 is an isosceles trapezoid, 𝑀𝑃 = 16𝑥 − 13, 𝑁𝑂 = 9𝑥 + 8, 𝑃𝑁 = 5𝑦 + 19, and 𝑀𝑂 = 12𝑦 − 37, solve for x and y. 8. If 𝑊𝑋𝑌𝑍 is an isosceles trapezoid, find each missing angle. 𝑚∠𝑊 = ____________ 𝑚∠𝑋 = ____________ 𝑚∠𝑌 = ____________ 𝑚∠𝑍 = ____________ Geometry Chapter 8: Quadrilaterals Use trapezoid 𝐴𝐵𝐶𝐷 for questions 9 – 12. 9. If 𝐴𝐵 = 14 and 𝐷𝐶 = 26, find 𝐸𝐹. 10. If 𝐴𝐵 = 7 and 𝐷𝐶 = 31, find 𝐸𝐹. 11. If 𝐸𝐹 = 22 and 𝐷𝐶 = 38, find 𝐴𝐵. 12. If 𝐴𝐵 = 41, and 𝐸𝐹 = 47, find 𝐷𝐶. 13. For trapezoid 𝑃𝑄𝑅𝑆, 𝑌 and 𝑍 are midpoints of the legs. Find 𝑌𝑍. 14. For trapezoid 𝑊𝑋𝑌𝑍, 𝑈 and 𝑉 are midpoints of the legs. Find 𝑈𝑉. 15. 𝑚∠𝐺𝐷𝐸 = ____________ 𝑚∠𝐷𝐸𝐻 = ____________ 𝑚∠𝐷𝐺𝐻 = ____________ Geometry Chapter 8: Quadrilaterals 16. If 𝑊𝑋 = 14 and 𝑊𝑅 = 8, find 𝑅𝑍. 17. 𝑚∠1 = ____________, 𝑚∠2 = ____________ 𝑚∠3 = ____________, 𝑚∠4 = ____________ 𝑚∠5 = ____________, 𝑚∠6 = ____________ 𝑚∠7 = ____________ 18. If 𝐴𝐶 = 38 and 𝐸𝐷 = 41, find 𝐶𝐷. 19. Find 𝑚∠𝐿. 20. Solve for x. Geometry Chapter 8: Quadrilaterals 21. Find 𝑚∠𝐹𝐺𝐽. 22. Find 𝑚∠𝑁𝑄𝑃. Closure: 1. What is the formula for the sum of the interior angles of a polygon? 2. What is the formula to find the measure of an interior angle of a regular polygon? 3. What is the sum of the exterior angles of any polygon? 4. What is the measure of each exterior angle of a regular nonagon? 5. Which quadrilaterals always have diagonals congruent? 6. Which quadrilaterals always have consecutive angles that are supplementary?