Bell Ringer Get out your notebook and prepare to take notes on Chapter 7 List five shapes you see in the classroom

Chapter 7

7.1 - Pairs of Angles (Page 303) Essential Questions: How do we identify types of angles? How can identifying types of angles allow us to find relationships among angles?

7.1 cont. Vertical angles Adjacent angles Formed by two intersecting lines Angles opposite one another are CONGRUENT Congruent - have the same measure Adjacent angles Common vertex and common side

7.1 cont. Example 1: Name a pair of adjacent angles and a pair of vertical angles in the figure below: 145° What is the measure of angle HGK?

7.1 cont. Supplementary angles Complementary angles Angles that add to 180 degrees Complementary angles Angles that add to 90 degrees

7.1 cont. Example 2: Find the measure of the supplement of the angle IGJ in the following figure: 35° What does the supplement you found represent in the figure?

7.1 cont. Perpendicular lines Two lines that intersect to form a right angle

7.1 cont. Example 3: In the following figure, if the measure of angle DKH is 73°, find the measures of the angles GKJ and JKF: 17° 73° 73°

7.1 - Closure How do we identify types of angles? Vertical angles, adjacent angles How can identifying types of angles allow us to find relationships among angles? Complementary/supplementary angles Identify perpendicular lines

7.1 - Homework Page 305-306, 2-32 even

Bell Ringer (7.2) Get out yesterday’s homework assignment Get out your notebook and prepare to take notes on Section 7.2 List two sets of parallel lines you see in the classroom

7.2 – Angles and Parallel Lines (Page 307) Essential Questions: What is a transversal?   What congruent angles are formed when a transversal intersects two parallel lines?

7.2 cont. Parallel Lines Transversal Equidistant at all points A line that intersects two or more lines at different points

7.2 cont. Corresponding Angles Alternate Interior Angles B Corresponding Angles Lie on same side of the transversal Have corresponding positions Are congruent ONLY when lines are parallel C D E F G H Alternate Interior Angles Lie within a pair of lines On opposite sides of the transversal Are congruent ONLY when lines are parallel E F G H

7.2 cont. Example 1: Identify each pair of corresponding angles and each pair of alternate interior angles in the following figure:

7.2 cont. Example 2: If p is parallel to q in the following figure, and the measure of angle 3 is 56°, find the measure of angle 6. = 56°

7.2 cont. Example 3: In the figure below, explain how you know ? Alternate interior angles are congruent, therefore, lines a and b are parallel.

7.2 - Closure What is a transversal? A line that intersects two or more lines at different points   What congruent angles are formed when a transversal intersects two parallel lines? Corresponding angles Alternate interior angles

7.2 - Homework Page 309-310, 2-28 even

Bell Ringer (7.3) Get out yesterday’s homework assignment Get out your notebook and prepare to take notes on Section 7.3 List five polygons you see in the classroom

7.3 – Congruent Polygons (Page 312) Essential Questions: Which parts of congruent figures can be congruent to each other? What are three ways we can demonstrate that two triangles are congruent?

7.3 cont. Congruent Polygons: Polygons that have the same size and shape Can be slid, flipped, or turned so that one fits exactly on top of the other Tick marks and arcs tell you which sides and angles are congruent NOTE: When naming congruent polygons, list corresponding vertices in the same order!! (i.e. ABC DEF)

7.3 cont. Example 1: In the diagram below, list the congruent parts of the two figures. Then write a congruence statement.

7.3 cont. Showing Triangles are Congruent: Use corresponding parts Use the following postulates: NOTE: Order of angles and sides is important!!

7.3 cont. Example 2: Show that the following pair of triangles are congruent: Angle Side Angle by

7.3 - Closure Which parts of congruent figures can be congruent to each other? Corresponding angles and sides What are three ways we can demonstrate that two triangles are congruent? SSS, SAS, ASA

7.3 - Homework Page 314-316, 2-28 even SKIP 22

Bell Ringer (7.4) Get out yesterday’s homework assignment Get out your notebook and prepare to take notes on Section 7.4 Answer the following question: What two characteristics do congruent polygons have in common?

7.4 – Classifying Triangles and Quadrilaterals (Page 318) Essential Question: How do we classify triangles and quadrilaterals?

(at least 2 congruent sides) 7.4 cont. Classifying Triangles: Use angles and sides 6 types: Acute (3 acute angles) Obtuse (1 obtuse angle) Right (1 right angle) Equilateral (3 congruent sides) Isosceles (at least 2 congruent sides) Scalene (no congruent sides)

isosceles acute triangle 7.4 cont. Example 1: Classify LMN by its sides and angles: 2 congruent sides 3 acute angles isosceles acute triangle

7.4 cont. Classifying Quadrilaterals: Use angles and sides Name quadrilaterals by listing vertices in consecutive order

7.4 cont. Example 2: How would you classify the following figure? Opposite sides are parallel Adjacent sides are not equal Parallelogram

7.4 - Closure How do we classify triangles and quadrilaterals? Triangles – angles or congruent sides Quadrilaterals – sides and angles

Page 320, 2-18 even 7.4 - Homework

Bell Ringer Get out yesterday’s homework assignment Think of any clarifying questions you may have about 7.1-7.4 Draw and label a trapezoid that contains a right angle.

Mimio Software Match the angle pair with the proper name

7.1-7.3 Review (Page 317)

7.4 Review Classify the following triangle according to its angles and sides: A triangle’s sides are all congruent and its angles all measure 60˚. Classify the triangle. Determine the best name for the following quadrilateral: What is the best name for a figure that has four sides congruent, corresponding angles parallel, and all four angles congruent?

QUIZ TOMORROW!! Sections 7.1-7.4 Homework: Page 346-347, 1-12, SKIP #5 Study: 7.1-7.4 Homework Notes Problems from today’s review

Bell Ringer (7.5) Get out your notebook and prepare to take notes on Section 7.5 Prepare to ask questions about the 7-1-7.4 quiz

7.5 – Angles and Polygons (Page 324) Essential Question: How do we find the interior angle measures of a polygon?

7.5 cont. Application: Common Polygons: Art, architecture, tile patterns Common Polygons: Polygon Name Number of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Dodecagon 12

7.5 cont. **Sum of the measures of the interior angles depends on the number of sides in the polygon** Polygon Angle Sum: For a polygon with n sides, the sum of the measures of the interior angles is as follows: °

7.5 cont. Octagon = 8 sides Example 1: Find the sum of the measures of the interior angles of an octagon. ° Octagon = 8 sides ° ° °

7.5 cont. Hexagon = 6 sides Example 2: Find the missing angle measure in the following hexagon: ° ° ° ° = sum of angle measures ° Hexagon = 6 sides

7.5 cont. Regular Polygons: All sides and angles congruent Equation for angle sum: °

7.5 cont. Example 3: A design tile is in the shape of a regular nonagon. Find the measure of each angle. ° ° = 140°

7.5 - Closure How do we find the interior angle measures of a polygon? For a polygon of n sides: For a regular polygon of n sides: ° °

7.5 - Homework Page 326-327, 2-28 even, SKIP 6, 22

Bell Ringer (7.6) Get out yesterday’s homework assignment Get out your notebook and prepare to take notes on Section 7.6 Find the measure of each angle of a regular polygon with 14 sides. Round to the nearest tenth. DO NOT LOSE THE FORMULA SHEET!!

7.6 – Areas of Polygons (Page 328) Essential Question: How do we find the area of a parallelogram, triangle, and trapezoid?

7.6 cont. Application: Area: Construction Farming Architecture Engineering Area: Number of square units a figure encloses

7.6 cont. Area of a Triangle: 𝑨= 𝟏 𝟐 𝒃𝒉 A = Area b = base h = height Any side of triangle can be the base Height of triangle is perpendicular distance between base and opposite vertex

7.6 cont. 𝐴= 1 2 𝑏ℎ 𝐴= 1 2 20 9.6 𝐴=96m2 Example 1: Find the area of the following triangle: 𝐴= 1 2 𝑏ℎ 𝐴= 1 2 20 9.6 𝐴=96m2

7.6 cont. 𝑨=𝒃𝒉 Area of a Parallelogram: A parallelogram can be divided into two congruent triangles Each triangle is half the area of the parallelogram

7.6 cont. 𝑨=𝒃𝒉 𝑨= 𝟏𝟎 𝟓 𝑨=𝟓𝟎cm2 Example 2: Find the area of the following parallelogram: 𝑨=𝒃𝒉 𝑨= 𝟏𝟎 𝟓 𝑨=𝟓𝟎cm2

7.6 cont. Area of a Trapezoid: 𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐 𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐 Note: b1 and b2 name two related variables and have no effect on the value of the variable

7.6 cont. Example 3: Find the area of the following trapezoid: 𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐 𝑨= 𝟏 𝟐 𝟔 𝟏𝟑+𝟏𝟓 𝑨=𝟖𝟒m2

7.6 - Closure How do we find the area of a parallelogram, triangle, and trapezoid? Parallelogram: 𝑨=𝒃𝒉 Triangle: 𝑨= 𝟏 𝟐 𝒃𝒉 Trapezoid: 𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐

7.6 - Homework Page 331, 1-11, 15-17

Bell Ringer (7.7) 𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐 𝑨= 𝟏 𝟐 𝟓 𝟔+𝟐.𝟓 𝑨=𝟐𝟏.𝟐𝟓 Get out yesterday’s homework assignment Get out your notebook and prepare to take notes on Section 7.7 Find the area of the following trapezoid: 𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐 𝑨= 𝟏 𝟐 𝟓 𝟔+𝟐.𝟓 𝑨=𝟐𝟏.𝟐𝟓

7.7 – Circumference and Area of a Circle (Page 336) Essential Questions: How do we find the circumference and the area of a circle? How can we use what we already know about area to find the area of irregular figures?

7.7 cont. Review: Area Radius Diameter

7.7 cont. 𝝅=𝟑.𝟏𝟒= 𝟐𝟐 𝟕

7.7 cont. Circumference: 𝑪=𝝅𝒅=𝟐𝝅𝒓 Area of a Circle: 𝑨=𝝅 𝒓 𝟐

7.7 cont. Example 1: Find the circumference and area of a circle with a diameter of 9.2 inches. Circumference: 𝑪=𝝅𝒅 𝑪=𝝅 𝟗.𝟐 𝑪≈𝟐𝟖.𝟗𝟏𝟒𝟑 in Area: 𝑨=𝝅 𝒓 𝟐 𝑨=𝝅 𝟒.𝟔 𝟐 𝑨≈𝟔𝟔.𝟓𝟎𝟐𝟗 in2 9.2 in.

7.7 cont. Example 2: Find the area of the following figure. Round to the nearest tenth. Step 1: Find area of rectangle. 𝑨=𝒍𝒘= 𝟐𝟎 𝟒𝟓 =𝟗𝟎𝟎 ft2 Step 2: Find the area of the semicircle. Entire circle: 𝑨=𝝅 𝒓 𝟐 Half of circle: 𝑨 𝑺 = 𝟏 𝟐 𝝅 𝒓 𝟐 𝑨 𝑺 = 𝟏 𝟐 𝝅 𝟏𝟓 𝟐 𝑨 𝑺 =𝟑𝟓𝟑.𝟔 ft2 Total Area: 𝟗𝟎𝟎+𝟑𝟓𝟑.𝟔=𝟏𝟐𝟓𝟑.𝟔 ft2

7.7 - Closure How do we find the circumference and the area of a circle? Circumference 𝑪=𝝅𝒅=𝟐𝝅𝒓 Area of a Circle: 𝑨=𝝅 𝒓 𝟐 How can we use what we already know about area to find the area of irregular figures? Split irregular figures into figures you know how to work with Find area of each figure you know and add them all together

Page 338-339 2-22 even, 26-30 7.7 - Homework

Bell Ringer Get out your 7.7 homework assignment Think of any clarifying questions you may have about Chapter 7 Find the radius, circumference, and area of a circle with a diameter of 10.5cm. Radius = 𝟏 𝟐 𝟏𝟎.𝟓 =𝟓.𝟐𝟓cm Circumference = 𝟐𝝅𝒓=𝟐𝝅 𝟓.𝟐𝟓 =𝟑𝟐.𝟗𝟖𝟔𝟕 Area = 𝝅 𝒓 𝟐 =𝝅 𝟓.𝟐𝟓 𝟐 =𝟖𝟓.𝟓𝟗𝟎𝟏

7.1, 7.2 - Review (Page 346)

7.3, 7.4 - Review (Page 347)

7.5 - Review (Page 347)

7.6, 7.7 - Review (Page 347)

Flatland/Big Bang Theory Clips

TEST TOMORROW!! Sections 7.1-7.7 Homework: Page 348, 1-29 Study: Notes Problems from today’s review