Post on 23-Jan-2016
description
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
Chapter 4
Congruent Triangles
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
Section 4-1 Congruent Figures
Review:What makes angles ?
same degree measurement
What makes segments ?same length
Can an angle be congruent to a segment?
Can a triangle be congruent to a square?
What makes figures congruent?
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.
Let’s Take a Look
Corresponding Angles
Corresponding Sides
Labeling Congruent Figures
Congruent figures must be labeled according to their corresponding parts.
Ex: Label the following congruent figures.
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
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!
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
Answers continued
12. R
13. ROHES
14. m ∠C15.4
16.∠ A17.The leaf in the lower left hand
corner is flipped over.
Applications to Proofs
When the definition of congruent triangles is used in a proof we write,
Corr. parts of Δ’s are
or CPCTC !!!
Current Goal:Identify/label CPCT.
Future Goal: Use parts to prove that figures are and vice versa.
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 ____.
Practice: Classwork Worksheet SKIP #3
Complete and we will go over.
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.
Homeworkpage 120
Written Exercises #1-11 (SKIP 10) & #14