1.6-6.1 Polygon notes Polygon: Examples: Nonexamples: Named by the letters of the vertices written in order polygon will be: oncave - Or: onvex- Regular Polygon:
1.6-6.1 Polygon notes iagonal is a segment that connects any two vertices not already connected by a side of the polygon. To find the sum of the angles inside a polygon we can use the following:
1.6-6.1 Polygon notes Ex. 1: Find the sum of the interior angles of an:. 11-gon.. 3x-gon. 15-gon Ex. 2: Find the number of sides of a regular polygon if the measure of an interior angle is:. 108. 170 If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is.
1.6-6.1 Polygon notes Ex. 1: Find the measures of an exterior angle of a:. regular dodecagon. polygon with 20 sides Ex. 2: Find the number of sides of the regular polygon with an exterior angle of:. 15. 60
1.6-6.1 Practice Name: Pd: ate: State if each shape is a polygon. If not, explain why it is not a polygon. 1. 2. 3. 4. State if each figure is regular or irregular: 9. 10. 11. 12. For each polygon name it by its number of sides, classify it as concave or convex, and state if it is regular or irregular: 13. 14. 15. 16. Find the sum of the measures of the interior angles of each convex polygon 1. 13-gon 2. heptagon 3. 24-gon 4. 4y-gon
1.6-6.1 Practice Find the number of sides in the regular polygon given the measure of an interior angle 9. 144 10. 120 11. 150 12. 176.4 Find the measure of an exterior angle and an interior angle of the regular polygon 17. quadrilateral 18. pentagon 19. decagon 20. 18-gon Find the number of sides of a regular polygon given an exterior angle measure 21. 7.5 22. 45 23. 22.5 24. 9
Parallelogram: Properties: Ex 1: Use parallelogram to find x, y, and z 6.2 Parallelograms Notes Ex 2: Use parallelogram to find x and y 2y + 3 20 3x 21 2y + 5 35 45 3x - 4
6-2 NME TE PERIO Study Guide and Intervention Parallelograms Sides and ngles of Parallelograms quadrilateral with both pairs of opposite sides parallel is a parallelogram. Here are four important properties of parallelograms. The opposite sides of a parallelogram are congruent. The opposite angles of a parallelogram are congruent. The consecutive angles of a parallelogram are supplementary. If PQRS is a parallelogram, then P Q S R and P S Q R P R and S Q P and S are supplementary; S and R are supplementary; R and Q are supplementary; Q and P are supplementary. If a parallelogram has one right If m P 90, then m Q 90, m R 90, and m S 90. angle, then it has four right angles. S P R Q Example If is a parallelogram, find a and b. and are opposite sides, so. 2a 34 a 17 and are opposite angles, so. 8b 112 b 14 2a 8b 34 112 Lesson 6-2 opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. Exercises Find x and y in each parallelogram. 1. 2. 3x 4y 3. 6x 4. 5. 6. 55 60 2y 3y 12 5x 8y 6x 88 3y 6x 12x 2y 30x 150 72x hapter 6 13 Glencoe Geometry
opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. 6-2 NME TE PERIO Study Guide and Intervention (continued) Parallelograms iagonals of Parallelograms Two important properties of parallelograms deal with their diagonals. If is a parallelogram, then: P The diagonals of a parallelogram bisect each other. Each diagonal separates a parallelogram into two congruent triangles. P P and P P and Example Find x and y in parallelogram. The diagonals bisect each other, so E E and E E. 6x 24 4y 18 x 4 y 4.5 Exercises Find x and y in each parallelogram. 18 E 6x 4y 24 1. 2. 3. 3x 4y 12 8 2y 28 4x 2x 60 4y 4. 5. 6. 10 30 y 3x 12 3x 2y x 4 y 17 omplete each statement about. Justify your answer. 7. E 8. E 9. 10. hapter 6 14 Glencoe Geometry
6.3 Tests for Parallelograms Notes If one of the following is true 1. 2. 3. 4. 5. Then the quadrilateral is a parallelogram. Find x and y so that the quadrilateral is a parallelogram 4y 6x-12 2x+36 6y-42 (4y+4) (7x) (56) (5y-26)
6.3 Tests for Parallelograms Notes re the following figures parallelograms? Justify your answer by telling why or why not. 1. 2. 8 7 8 7 10 10 3. 4. 12 12 5. 6. 82 o 98 o 98 o 82 o
6.3 Homework
efinition: Properties: is a rectangle. Find x and if = 6x + 14 and = 9x + 5 6.4 Rectangle Notes 1 E 2 3 Use the rectangle to find x and y given: m 1 = 9x + 20 4 m 2 = 4x + 5 m 3 = 4y + 4 m 4 = y + 28
NME TE PERIO 6-4 Skills Practice Rectangles LGER is a rectangle. E 1. If 2x 13 and 4x 1, find x. 2. If x 3 and 3x 19, find. 3. If E 3x 3 and E 5x 15, find. 4. If E 6x 7 and E 4x 9, find. 5. If m 2x 4 and m 3x 1, find x. 6. If m 7x 1 and m 9x 7, find m. 7. If m x 2 7 and m 4x 5, find x. 8. If m x 2 3 and m x 15, find m. opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. PRST is a rectangle. Find each measure if m 1 50. 9. m 2 10. m 3 11. m 4 12. m 5 13. m 6 14. m 7 15. m 8 16. m 9 OORINTE GEOMETRY etermine whether TUXY is a rectangle given each set of vertices. Justify your answer. 17. T( 3, 2), U( 4, 2), X(2, 4), Y(3, 0) 18. T( 6, 3), U(0, 6), X(2, 2), Y( 4, 1) P 1 2 3 R 4 9 7 8 6 5 T S Lesson 6-4 19. T(4, 1), U(3, 1), X( 3, 2), Y( 2, 4) hapter 6 29 Glencoe Geometry
efinition: Properties: Use Rhombus to find x and if: = 5x 4 and E = 2x + 6 6.5 Rhombus (Rhombi) Notes Use Rhombus to m E = 6x 12 find x if: m E = 4x 8 E E
efinition: Properties: Use Square to find x and y if: m E = 2x + 32 = 4y + 3 6.5 Square Notes Use Square to m E = 6x 5 find x if: m E = 4x + 23 = 39 E E
6.5 Homework
6.6 Trapezoid Notes Trapezoid If the legs are congruent then the trapezoid is an Median Ex 1: If = 17 and = 29 Ex 2: If = 22 and XY = 15 Find XY Find
6.6 Trapezoid Notes Ex 3: WXYZ is an Isosceles Trapezoid Find the median, X, and Y. W 30 X Z 14 Y Ex 4: For trapezoid, G and H are midpoints of the legs. Find,, and G 36 H 54 Ex 5: JKLM is an Isosceles Trapezoid with median QR Find LM, J, and K J 24 K Q 29 R M 54 L
6.6 Homework is the median of trapezoid HJKL. Find each indicated value 1. Find MN if HJ = 32 and LK = 60 2. Find LK if HJ = 18 and MN = 28 3. Find MN if HJ + LK = 42 4. Find m LMN if m LHJ = 116 5. Find m JKL if HJKL is isosceles and m HLK = 62 6. Find HJ if MN = 5x + 6, HJ = 3x + 6, and LK = 8x