FiveMinute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts:


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1 FiveMinute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Perimeter, Circumference, and Area Example 2: Find Perimeter and Area Example 3: Standardized Test Example: Largest Area Example 4: Perimeter and Area on the Coordinate Plane 1
2 Over Lesson 1 5 Refer to the figure. Name two acute vertical angles. Refer to the figure. Name a linear pair whose vertex is E. Refer to the figure. Name an angle supplementary to BEC. 1 and 2 are a pair of supplementary angles, and the measure of 1 is twice the measure of 2. Find the measures of both angles. If RS is perpendicular to ST and SV is the angle bisector of RST, what is m TSV? Over Lesson 1 5 Refer to the figure. Name two acute vertical angles. A. AED and BEC B. AEB and DEC C. DEA and DEC D. BEC and BEA 2
3 Over Lesson 1 5 Refer to the figure. Name two acute vertical angles. A. AED and BEC B. AEB and DEC C. DEA and DEC D. BEC and BEA Over Lesson 1 5 Refer to the figure. Name a linear pair whose vertex is E. A. AED, BEC B. AEB, BEA C. CED, AEB D. AEB, AED 3
4 Over Lesson 1 5 Refer to the figure. Name an angle supplementary to BEC. A. AEB B. AED C. AEC D. CEB Over Lesson and 2 are a pair of supplementary angles, and the measure of 1 is twice the measure of 2. Find the measures of both angles. A. m 1 = 60, m 2 = 120 B. m 1 = 100, m 2 = 80 C. m 1 = 100, m 2 = 50 D. m 1 = 120, m 2 = 60 4
5 Over Lesson 1 5 If RS is perpendicular to ST and SV is the angle bisector of RST, what is m TSV? A. 30 B. 45 C. 55 D. 60 Content Standards G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision. 5
6 You measured onedimensional figures. Identify and name polygons. Find perimeter, circumference, and area of twodimensional figures. polygon vertex of a polygon concave convex ngon equilateral polygon equiangular polygon regular polygon perimeter circumference area 6
7 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular. There are 4 sides, so this is a quadrilateral. No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex. The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular 7
8 Name and Classify Polygons B. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular. There are 9 sides, so this is a nonagon. Lines containing some of the sides will pass through the interior of the nonagon, so it is concave. Since the polygon is concave, it must be irregular. Answer: nonagon, concave, irregular A. Name the polygon by the number of sides. Then classify it as convex or concave and regular or irregular. A. triangle, concave, regular B. triangle, convex, irregular C. quadrilateral, convex, regular D. triangle, convex, regular 8
9 B. Name the polygon by the number of sides. Then classify it as convex or concave and regular or irregular. A. quadrilateral, convex, irregular B. pentagon, convex, irregular C. quadrilateral, convex, regular D. quadrilateral, concave, irregular 9
10 Find Perimeter and Area A. Find the perimeter and area of the figure. P = 2l + 2w = 2(4.6) + 2(2.3) A = lw = (4.6)(2.3) = 13.8 = Answer: The perimeter of the rectangle is 13.8 cm. The area of the rectangle is cm 2. Find Perimeter and Area B. Find the circumference and area of the figure. = 8π = = (4) =16 Answer: The circumference of the circle is 8π inches The area of the circle is 16π square inches. 10
11 A. Find the perimeter and area of the figure. A. P = 12.4 cm, A = 24.8 cm 2 B. P = 24.8 cm, A = cm 2 C. P = cm, A = cm 2 D. P = 24.4 cm, A = 32.3 cm 2 B. Find the circumference and area of the figure. A. C = 50.3 m, A = 25.1 m 2 B. C = 50.3 m, A = m 2 C. C = 16π m, A = 64π m 2 D. C = 64π m, A = 16π m 2 11
12 Terri has 19 feet of tape to mark an area in the classroom where the students may read. Which of these shapes has a perimeter or circumference that would use most or all of the tape? A square with side length of 5 feet B circle with the radius of 3 feet C right triangle with each leg length of 6 feet D rectangle with a length of 8 feet and a width of 3 feet Read the Test Item Largest Area You are asked to compare the perimeters or circumference of four different shapes. C = 2πr r = 3 = 2π(3) = 6π feet Largest Area Find each perimeter or circumference. Square P = 4s s = 5 Right Triangle c 2 = a 2 + b 2 a = b = 6 = 4(5) = = 72 =6 2 = 20 feet P = a + b + c Circle = The only shape for which Terri has enough tape is the circle feet Rectangle P = 2l + 2w = 2(8) + 2(3) l = 8, w = 3 = 22 feet 12
13 Each of the following shapes has a perimeter of about 88 inches. Which one has the greatest area? A. a rectangle with a length of 26 inches and a width of 18 inches B. a square with side length of 22 inches C. a right triangle with each leg length of 26 inches D. a circle with radius of 14 inches Perimeter and Area on the Coordinate Plane Find the perimeter (to the nearest unit) and area of a pentagon ABCDE with A(0, 4), B(4, 0), C(3, 4), D( 3, 4), and E( 3, 1). 13
14 Step 1 Notice CD = 6 and DE = 5 To find AB, BC and EA use = Δ + Δ = = 16+16= 32 =4 2 Perimeter and Area on the Coordinate Plane = = 1+16= 17 = 17 = = 9+9= 18 =3 2 Step 1 So =4 2 = 17 =6 =5 =3 2 Perimeter and Area on the Coordinate Plane And the perimeter of pentagon ABCDE is units (or about 25 units). Note that =7 2 14
15 Perimeter and Area on the Coordinate Plane Step 2 Divide the pentagon into two triangles and a rectangle. Find the area of the triangles. Area of Triangle 1 Find the area of the rectangle. = =9 Area of Triangle 2 = =5 2 A = (5)(6) = 30 The area of pentagon ABCDE is or 41.5 square units. Answer: The perimeter is about 25 units and the area is 41.5 square units. Find the perimeter of quadrilateral WXYZ with W(2, 4), X( 3, 3), Y( 1, 0), and Z(3, 1). A. + + B C. D. 15
16 16
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