answers
DESCRIPTION
Answers. 1. yes 2. no 3. yes 4. no 5. yes 1. mTRANSCRIPT
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Answers
1. yes 2. no 3. yes 4. no 5. yes
1. m<A = 45; m<B =45; m<C=90
right isosceles
2. m<K =80; m<L = 60; m<M = 40;acute scalene
3. 120
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Chapter 4
Congruent Triangles
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Agenda and ObjectivesAgendaNotes, practice, review 4-1Notes, practice, review 4-2
Objectives Identify congruent figures and corresponding
partsProve that two triangles are congruentProve that triangles are congruent using the
SSS and SAS Congruence Postulates
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Section 4-1 Congruent Figures
Review:What makes angles ?
same degree measurement
What makes segments ?same length
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Can an angle be congruent to a segment?
Can a triangle be congruent to a square?
What makes figures congruent?
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Congruent Figures
Two figures that have the same size and shape.
If figures are congruent then they have congruent angles and congruent sides or parts.
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Let’s Take a Look
Corresponding Angles
Corresponding Sides
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Labeling Congruent Figures
Congruent figures must be labeled according to their corresponding parts.
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Ex: Label the following congruent figures.
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Possible Answers
Δ 1 Δ 2 Δ ABC Δ EFD Δ BCA Δ FDEΔ CBA Δ DFE
Δ 2 Δ 3
Δ EFD Δ HGI
Δ FDE Δ GHI
Δ DEF Δ IHG
Δ 1 Δ 3
Δ ABC Δ HGI
Δ BCA Δ GIH
Δ CAB Δ IHG
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Ex: Given: Δ CAT Δ DOGWhich angles are congruent to one another?
C and DA and O T and G
Which sides are congruent to one another?CA and DO; AC and ODAT and OG; TA and GOTC and GD; CT and DG
To help solve, draw a picture!
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You try..Page 119 1-9, 12-17
Please work independently
Answers 1. FI, WE; IN, EB; FN, WB
2. ∠ F, ∠ W; ∠ I, ∠ E; ∠ N, ∠ B3. YES
4. NO
5. ∆CDO6. ∠C7. CO8. DO9. Yes because AO = OC and DO = OB
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Answers continued
12. R
13. ROHES
14. m ∠C15.4
16.∠ A17.The leaf in the lower left hand
corner is flipped over.
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Applications to Proofs
When the definition of congruent triangles is used in a proof we write,
Corr. parts of Δ’s are
or CPCTC !!!
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Current Goal:Identify/label CPCT.
Future Goal: Use parts to prove that figures are and vice versa.
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Example
The two triangles shown are congruent. Complete…∆STO ≅ ________∠S ≅ ____ because ____.SO ≅ ___ because ____.Then point O is the midpoint of ____.∠T ≅ ___ because ___.Then ST || RK because ____.
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Practice: Classwork Worksheet SKIP #3
Complete and we will go over.
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Closure to 4.1
On a little piece of paper write never, sometimes or always.
1. An acute triangle is ____ congruent to an obtuse triangle.
2. A polygon is ____ congruent to itself.
3. A right triangle is _____ congruent to another right triangle.
4. If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y.5. If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.
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Homeworkpage 120
Written Exercises #1-11 (SKIP 10) & #14