Chapter 4
Download
1 / 10

Chapter 4 - PowerPoint PPT Presentation


  • 65 Views
  • Uploaded on

Chapter 4. 4.2 Congruence & Triangles. Objectives/Assignment. Identify congruent figures and corresponding parts Prove that two triangles are congruent Assignment: 1-29 all, quiz page 210. Goal 1: Identifying Congruent Figures.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Chapter 4' - brittany-wynn


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Chapter 4

Chapter 4

4.2 Congruence & Triangles


Objectives assignment
Objectives/Assignment

  • Identify congruent figures and corresponding parts

  • Prove that two triangles are congruent

  • Assignment: 1-29 all, quiz page 210


Goal 1 identifying congruent figures
Goal 1: Identifying Congruent Figures

  • Two geometric figures are congruent if they have exactly the same size and shape.

  • When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.


Abc pqr
ABC =̃ PQR

B

Q

C

P

R

A

What are the corresponding angles?

What are the corresponding sides?

A & P

B & Q

C & R

AB & PQ

BC & QR

CA & RP


Theorem 4 3 third angles theorem
Theorem 4.3: Third Angles Theorem

  • If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.


Goal 2 proving triangles are congruent
Goal 2: Proving Triangles are Congruent

  • Given: seg RP  seg MN, seg PQ  seg NQ , seg RQ  seg MQ, mP=92o and mN is 92o.Prove: ΔRQP ΔMQN

R

N

92o

Q

92o

M

P


Given: seg RP  seg MN, seg PQ  seg NQ , seg RQ  seg MQ, mP=92o and mN is 92o.Prove: ΔRQP ΔMQN

Statements Reasons

1.seg RP  seg MN 1. given

seg PQ  seg NQ

seg RQ  seg MQ

2. mP=mN 2. trans. prop =

3. P N 3. def of s

4. RQP MQN 4. vert s thm

5. R M 5. 3rds thm

6. ΔRQP Δ MQN 6. def of  Δs


Theorem 4 4 properties of congruent triangles
Theorem 4.4: Properties of Congruent Triangles

  • Reflexive Property of Congruent Triangles: Every triangle is congruent to itself

  • Symmetric Property of Congruent Triangles: If ABC =̃ DEF, then DEF =̃ ABC

  • Transitive Property of Congruent Triangles:

    If ABC =̃ DEF and DEF =̃ JKL, than

    ABC =̃ JKL


Practice problems
Practice Problems

  • Name the congruent figures

  • Given M =̃ G and P =̃ H, find the value of x.

E

B

D

A

C

F

(2X-50)°

H

M

142°

N

J

P

G

24°


More practice problems
More Practice Problems

Given that N =̃ R and L =̃ S, find the value of x.

Given that LMN =̃ PQR, answer the following:

mP= QR =̃

mM= LN =̃

mR=

mN=

R

M

S

(2X+30)°

N

55°

65°

L

T

P

N

Q

45°

R

L

105°

M


ad