Geo 10 Ch Angles of a Triangle. (A) A triangle is a figure formed by 3 joining 3
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1 Geo 0 h ngles of a Triangle () triangle is a figure formed b joining raw a picture and describe each of the following triangles.. Scalene 4. cute. Isoceles 5. Obtuse. Equilateral 6. Right () Given triangle. raw a line throught that is parallel to segment. Show algebraicall how the sum of the angles of the triangle equal 80 degrees. EX. () Find () Find In an equilateral triangle
2 Geo 0 h.4-.5 () Find a What must be true about angle in a right triangle? a (4) Find and onclusion? 4 4 () Show algebraicall the relationship between the eterior angle and angles and.
3 Geo 0 h.4-.5 E: () Find and () Find z 0 () Find and (a) (b) (c) (d) b a 0
4 Geo 0 h (e) Find? (f) Find,, z z 80? (g) a 4 b d c e f Proofs. Given:, < 4 Prove: bisects < 5 6 4
5 Geo 0 h Given:, 4 Prove: 4.
6 Geo 0 h Polgon = "man angles" Name each polgon and find the measure of all the angles. Name Sum = 80 = 80 = 80 = 80 See the pattern? The sum of the measures of the angles of a conve polgon with n sides is e d a b c Find the sum of the eterior angles. The sum of the measures of the eterior angles of an polgon, one angle at each verte, is. What if the polgon is a regular polgon? What do ou know about the angles? Int angles = Et angles = What is the relationship between the interior and eterior angles of an polgon?
7 Geo 0 h EXMPLES Find the interior sum, eterior sum, interior and eterior angles for each regular polgon with n sides. () Number of sides (n) Interior sum Eterior sum Interior angle Eterior angle Which is easier to find, an interior angle or an eterior angle? ) n interior angle of a regular polgon = 60. How man side does it have? ) Fill in the blanks number of sides 9 5 et angle 6 8 interior angle 65 78
8 Geo 0 h LSS REVIEW.4 Find the value for the variable(s).. z 0 +0 = = z = =. = = 4. a b d 4 c e f a = b = c = d = e = f =
9 Geo 0 h Review Questions F G. Given: bisects, m HF, H 60 GH H 60 E Find: m FH = m GH = m HE = m HG = m H = m H = m FHG= m H = m H =. Given: PR bisects SPQ, PS SQ Find: RQ PQ, m SPT 6 P S T R Q m = m = m = m 4 = m 5 = m 6 = ) Find the sum of the measures of the marked angles. Sum = 4) Find the measure of each interior angle of a regular 5-gon.
10 Geo 0 h Review ont. 5. If a polgon has sides, find the sum of the interior angles. 6. If a regular polgon has 6 sides, find each interior angle. 7. If 7 eterior angles of an octagon each measure 4, what is the measure of the 8 th angle? 8. The second angle of a triangle is three times the first, and the third angle is nine less than five times the first. Find the measure of each angle of the triangle. 9. a) if m g = 8, m e = 7, then m i =. b) if m g = 46, m i = 79, then m h =. k g e h f i 0. For regular polgons, fill in the following chart completel. Number of sides 4 Each Interior 7 70 Each Eterior Solve for the variable(s) in each drawing z z 0
11 Geo 0 h *5.. z = = z = = = Proofs: 6. Given: m = m E Prove: m = m F E F 7. Given: RU ST, R T Prove RS UT : R S U 4 T m 4 8. Given: m n; Prove: a b n a b
12 Geo 0 h Given F, E Prove: E F E E Given: E, E Given: < < Prove: < <8 Prove: < <E *. Given : l m, find 78 l 5 m. Given:,, E Prove: E
13 Geo 0 h.4-.5 * Given:, < <4 Prove: 5 *5. < = <, marked lines are parallel find < 0
14 Geo 0 h Given: bisects < Prove: *7. Given: < = < Prove: <4 = < 4 5 6
15 Geo 0 h Review nswers: = 6 =6 =64 4=8 5=5 6=64. NONE , 6, a) 5 b) =4 =47. ==70 z=6. =0 =0 z= , 40, 0 5. =90 =9 z=9 5. =8, = 5. < = 40
16 Geo 0 h EFINITIONS H EQUILTERL TRINGLE. REGULR POLYGON THEOREMS/OROLLRIES, ET THIR NGLE OROLLRY NGLES IN EQUILTERL TRINGLE UTE NGLES IN RIGHT TRINGLE ET THE SUM OF INTERIOR NGLES THE SUM OF EXTERIOR NGLES TO FIN EH INTERIOR NGLE IN REG. POLY TO FIN EH EXTERIOR NGLE IN REG. POLY.
17 Geo 0 h SUPPLEMENTRY PROLEMS. Given two triangles where two angles in each are equal to each other. What can ou sa about the third angles?. Given the following diagram, < is called an eterior angle of the triangle, being made up of one side of the triangle and an etension of another. How man eterior angles can ou find at each verte of the triangle? (a) If the m< = 50 and the m< = 0. Find the m< and the m<. (b) If the m< = and m< =, find the m> and come up for a rule about each of the eterior angles of a triangle?. The word polgon means man angles. Each polgon below is formed b coplanar segments, called sides, and we will denote each side as n. Name each polgon and find the measure of all the angles. Name Sum 80 = 80 = 80 = 80 See the pattern? What if I have a polgon with n sides, what is the sum of the interior angles? Give me a rule to follow for the sum of the interior angles of a polgon with n sides. 4. polgon with equal sides and equal angles is called regular. How could ou find each angle of a regular polgon?
18 Geo 0 h In the diagram, find the sum of the eterior angles, one at each verte Since the angles of a triangle add up to 80, a) make up a triangle and find the sum of the eterior angles, one at each verte. b) Make up a quadrilateral and find the sum of the eterior angles, one at each verte. c) Make up a heagon and find the sum of the eterior angles, one at each verte. d) What have ou observed?
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