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Challenge! Ka-Broom! Rules:
Each member of your team must catch 2! First team to complete the task gets 5 points, 2nd team gets 3, 3rd team gets 2!
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Unit 4 TRIANGLE FUN
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Learning Targets Lesson 4-1
I can use the angle sum theorem I can use the angle sum theorem I can the exterior angle theorem I can the exterior angle theorem Learning Targets Lesson 4-1
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sum angles 180°
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30° m∠1 = 28° m∠1 = 120°
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58° 32° 32° 58° m∠1 = 56° m∠2 = 56° m∠3 = 74°
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remote interior exterior not
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exterior angle sum remote interior angles m∠1 = m∠A + m∠B
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m∠1 = 115°
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2x + 95 = 145 2x = 50 x = 25
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140° 40° 65° 75° 115°
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55° 55° 70°
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125° 55° 95°
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ASSIGNMENT: 4-1Worksheet
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4.2 Congruent Triangles Learning Target:
I can name and label corresponding parts of congruent triangles.
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vertices Naming Triangles Triangles are named by their ______________.
Instruction Naming Triangles Triangles are named by their ______________. vertices A B C
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size shape
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Angle Measure Betweenness Collinearity Distance
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m∠A = m∠J AB = JK m∠B = m∠K BC = KL m∠C = m∠L AC = JL
Match up the letters in the same “position” AND look at the ‘tick marks’ in the picture! Match the congruent pieces!
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Warm Up
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I can recognize and use the SSS, SAS, ASA, AAS, and HL Postulates to see if triangles are the same.
Lesson 4.3
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CAN’T USE!!! 40 40 50 50
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CAN’T USE!!! 7 7 6 6 40° 40°
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SAS ∆DNV ≅ ∆BCX
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SSS ∆TRS ≅ ∆SUT
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HL ∆JKL ≅ ∆MNP
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AAS ∆NJK ≅ ∆LMK
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Your turn! Try e-h! SAS ∆CDA ≅ ∆BDA
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ASA ∆RST ≅ ∆UVT
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AAS ∆RUT ≅ ∆RST
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SAS ∆FJH ≅ ∆GHJ
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A M R C W G MG ≅ AC
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D X G K Y Z YZ ≅ DK
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D A E F B C ∠B ≅ ∠E or ∠C ≅ ∠F
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“Swimming through triangles” worksheet, both sides (Pages 3 – 4)
ASSIGNMENT: “Swimming through triangles” worksheet, both sides (Pages 3 – 4)
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Warm Up
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PROOFS! Lesson 4.4
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Given Given Reflexive TS ≅ TS ∆RST ≅ ∆UTS SSS
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∠RSU ≅ ∠TSU US ≅ US ∆RSU ≅ ∆TSU Given Given Def’n of angle bisector
Reflexive US ≅ US SAS ∆RSU ≅ ∆TSU
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Your Turn…
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Given Given Reflexive BD ≅ BD SSS ∆ABD ≅ ∆CBD CPCTC ∠A ≅ ∠C
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DF ≅ DF AIA ≅↔ || lines ∠EDF ≅ ∠GFD ∆EDF ≅ ∆GFD DG ≅ FE Given Given
Reflexive DF ≅ DF AIA ≅↔ || lines ∠EDF ≅ ∠GFD AAS ∆EDF ≅ ∆GFD CPCTC DG ≅ FE
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Given Given Reflexive BC ≅ BC ∆BAC ≅ ∆BDC HL CPCTC ∠A ≅ ∠D
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Your Turn… BC || AD BC ≅ AD BD ≅ BD ∠CBD ≅ ∠ADB AIA ≅↔ || lines
Given BC ≅ AD Given BD ≅ BD Reflexive ∠CBD ≅ ∠ADB AIA ≅↔ || lines ∆ABD ≅ ∆CDB SAS
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Your Turn… ∠D ≅ ∠F GE bisects ∠DEF GE ≅ GE ∠DEG ≅ ∠FEG ∆DEG ≅ ∆FEG
Given GE bisects ∠DEF Given GE ≅ GE Reflexive Def. of angle bisector ∠DEG ≅ ∠FEG ∆DEG ≅ ∆FEG AAS DE ≅ FE CPCTC
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Group Activity Please put your tables into groups of 4 (push 2 tables together!) We will rotate through 4 stations to fill out proofs You will have approximately 4 minutes per station. Work quickly but accurately!
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Warm Up
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4.5 Isosceles and Equilateral Triangles
Learning Targets I can use properties of isosceles triangles. I can use properties of equilateral triangles.
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Vertex angle 2 congruent sides opposite 2 congruent sides Base angles
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2 sides congruent opposite congruent
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∠I ≅ ∠N FX ≅ OX Small triangle: Use 3 letters to name the angles! SV ≅ ST ∠SRT ≅ ∠STR
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40 + 2x + 2x = 180 40 + 4x = 180 4x = 140 x = 35 2x + 6 = 3x – 6 6 = x – 6 12 = x
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L 2x + 1 = 3x – 2 2x + 1 3x – 2 1 = x – 2 x = 3 N M 5x – 2
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Warm Up
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equiangular 60 6x = 60 6x – 5 = 5x – 5 = -1x x = 10 5 = x
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F 2x – 2 = x + 5 2x – 2 x + 5 x – 2 = 5 x = 7 H G 3x – 9
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CD ≅ CG DE ≅ GF ∠D ≅ ∠G ∆CDE ≅ ∆CGF CE ≅ CF Isosceles Given Given
So base angles are congruent! CD ≅ CG Given Given DE ≅ GF ∠D ≅ ∠G ITT ∆CDE ≅ ∆CGF SAS CE ≅ CF CPCTC
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4.6 Constructing Triangles
Use the construction instructions to work through the constructions at your table. Please raise your hand if you need assistance!
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