HW: P 98-99 18-28 even, 29, and 30.

5t-12=t+20 4t=32 T=8 Sides = 28, 28, 24 3t=5t-12 T=6 Sides = 18, 18, and 26 3t=t+20 T=10 Sides= 30,30, and 38

20. The measure of one angle of a triangle is 28 more than the measure of the smallest angle of the triangle. The measure of the third angle is twice the measure of the smallest angle. Find all three measures. 𝑥=𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑎𝑛𝑔𝑙𝑒 4𝑥+28=180 4𝑥=152 𝑥=38 𝑥+28=66 2𝑥=76 2𝑥=3𝑟𝑑 𝑎𝑛𝑔𝑙𝑒 𝑥+28=𝑜𝑛𝑒 𝑎𝑛𝑔𝑙𝑒

22 𝐼𝑛 .∆𝑅𝑆𝑇, 𝑚∠𝑅=90, 𝑚∠𝑆>20. 𝑊ℎ𝑎𝑡 𝑐𝑎𝑛 𝑦𝑜𝑢 𝑠𝑎𝑦 𝑎𝑏𝑜𝑢𝑡 𝑚∠𝑇? T must be less than 70 a. IFG=20 EGF= 60 IGF=30 FIG=130 b. EGF=50 IGF= 25 IFG= 25 FIG= 130 c.

1=35

2=125 55 1=35 95 55 55

𝐺𝐾 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐽𝐺𝐼 ∠1= 1 2 𝑚∠𝐽𝐺𝐼 𝑚∠𝐽𝐺𝐼=𝑚∠𝐻+𝑚∠𝐼 𝑚∠𝐻=𝑚∠𝐼 𝑚∠𝐽𝐺𝐼=𝑚𝐻+𝑚𝐻 𝑚∠𝐻= 1 2 𝑚∠𝐽𝐺𝐼 𝑚∠𝐻=𝑚∠1 𝐺𝐾 ∥ 𝐻𝐼 𝐺𝑖𝑣𝑒𝑛 𝐼𝑓 𝑎𝑛 𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑏𝑖𝑠𝑒𝑐𝑡𝑒𝑑, 𝑖𝑡 𝑖𝑠 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑖𝑛𝑡𝑜 2 𝑐𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡 𝑎𝑛𝑔𝑙𝑒𝑠, 𝑒𝑎𝑐ℎ ½ the measure of the original. 𝑇ℎ𝑒 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑎 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑐𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡 𝑡𝑜 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑟𝑒𝑚𝑜𝑡𝑒 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒𝑠 𝐺𝑖𝑣𝑒𝑛 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑃𝑟𝑜𝑝 𝑜𝑓= 𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑣𝑒 𝑃𝑟𝑜𝑝 If 2 lines are intersected by a transversal, and the corr angles are congruent, then the two lines are parallel.

𝑥+2𝑦+90=125 𝑥=35−2𝑦 2 35−2𝑦 +𝑦+125=180 70−4𝑦+𝑦+125=180 195−3𝑦=180 15=3𝑦 𝑦=5; 𝑥+10+90=125 𝑥=25 10𝑥+𝑦−𝑦+100=180 10𝑥=80 𝑥=8 2𝑥+𝑦=5𝑥−𝑦 16+𝑦=40−𝑦 2𝑦=24 𝑦=12 𝑦=15

Polygons

Finding angle measures in polygons A closed plane figure with at least three sides that are segments. The sides ONLY intersect at endpoints. No adjacent sides are collinear.

Segments intersect at a point other than their endpoint Figure is not closed Segments intersect at a point other than their endpoint Curve,not a line…

Concave- at least one diagonal will be outside of the polygon Classification of Polygons as convex or concave… Concave- at least one diagonal will be outside of the polygon Convex – all diagonals will be within the polygon ALL POLYGONS DISCUSSED IN THIS TEXT BOOK WILL BE CONVEX POLYGONS

Naming a polygon Start at any vertex, and list the vertices consecutively in either a clockwise or counterclockwise direction. Examples: Polygon Sides Angles

Polygon ABE, (or BEA, EAB, EBA, BAE, AEB) Sides Angles Name the three polygons below, their angles and their sides. Polygon ABE, (or BEA, EAB, EBA, BAE, AEB) Sides Angles Polygon CBED, (or BCDE,CDEB, etc) Sides Angles Polygon CBAED, (or BCDEA,CDEAB, etc) Sides Angles

A diagonal of a polygon is a segment joining two nonconsecutive vertices.

A polygon can be equilateral or equiangular A polygon can be equilateral or equiangular. If a polygon is both, it is called a regular polygon. Equiangular Equilateral AND Equiangular = REGULAR Equilateral

Classification of Polygons by their number of sides Name 3 triangle 4 quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octogon 9 Nonagon 10 Decagon 12 Dodecagon N N-gon Sides Name 3 4 5 6 7 8 9 10 12 n

Drawing triangles inside polygons… Choose a point at one vertex, and draw a line to every other vertex that is not collinear with the original point.

Number of Triangles Formed Sum of Interior Angle Measures Polygon Number of Sides Number of Triangles Formed Sum of Interior Angle Measures triangle quadrilateral pentagon hexagon heptagon n-gon Polygon Number of Sides Number of Triangles Formed Sum of Interior Angle Measures triangle quadrilateral pentagon hexagon heptagon n-gon

Number of Triangles Formed Sum of Interior Angle Measures Polygon Number of Sides Number of Triangles Formed Sum of Interior Angle Measures triangle 3 1 1•180 quadrilateral 4 2 2•180 pentagon 5 3•180 hexagon 6 4•180 heptagon 7 5•180 n-gon n-2 (n-2)•180 Polygon Number of Sides Number of Triangles Formed Sum of Interior Angle Measures triangle quadrilateral pentagon hexagon heptagon n-gon

Theorem 3-13: The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180. Example: What is the sum of the measures of the angles of a 13-gon?

Find the missing angle measures:

The sum of the measures of the angles of a polygon with n sides is 1080. How many sides does the polygon have?

Exterior Angles of a Polygon Polygon exterior angle sum theorem: The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360o.

Find the measure of each angle:

Homework: 1-6, 9-17 Alg Rev #11 Due Friday