FG
This presentation is the property of its rightful owner.
Sponsored Links
1 / 21

Warm Up 1. Name all sides and angles of ∆ FGH . 2. What is true about  K and  L ? Why? PowerPoint PPT Presentation


  • 32 Views
  • Uploaded on
  • Presentation posted in: General

FG , GH , FH ,  F ,  G ,  H. Warm Up 1. Name all sides and angles of ∆ FGH . 2. What is true about  K and  L ? Why? 3. What does it mean for two segments to be congruent?.  ;Third  s Thm. They have the same length.

Download Presentation

Warm Up 1. Name all sides and angles of ∆ FGH . 2. What is true about  K and  L ? Why?

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


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

FG, GH, FH, F, G, H

Warm Up

1.Name all sides and angles of ∆FGH.

2. What is true about K and L? Why?

3.What does it mean for two segments to be congruent?

 ;Third s Thm.

They have the same length.


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides.

Two polygons are congruent polygons if and only if their corresponding sides are congruent. Thus triangles that are the same size and shape are congruent.


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS.

In a congruence statement, the order of the vertices indicates the corresponding parts.


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Helpful Hint

When you write a statement such as ABCDEF, you are also stating which parts are congruent.


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Sides: PQ ST, QR  TW, PR  SW

Example 1: Naming Congruent Corresponding Parts

Given: ∆PQR ∆STW

Identify all pairs of corresponding congruent parts.

Angles: P  S, Q  T, R  W


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Sides: LM EF, MN  FG, NP  GH, LP  EH

Check It Out! Example 1

If polygon LMNP polygon EFGH, identify all pairs of corresponding congruent parts.

Angles: L  E, M  F, N  G, P  H


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Example 2A: Using Corresponding Parts of Congruent Triangles

Given: ∆ABC ∆DBC.

Find the value of x.

BCA andBCD are rt. s.

Def. of  lines.

BCA BCD

Rt. Thm.

Def. of  s

mBCA = mBCD

Substitute values for mBCA and mBCD.

(2x – 16)° = 90°

Add 16 to both sides.

2x = 106

x = 53

Divide both sides by 2.


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Example 2B: Using Corresponding Parts of Congruent Triangles

Given: ∆ABC ∆DBC.

Find mDBC.

∆ Sum Thm.

mABC + mBCA + mA = 180°

Substitute values for mBCA and mA.

mABC + 90 + 49.3 = 180

Simplify.

mABC + 139.3 = 180

Subtract 139.3 from both sides.

mABC = 40.7

DBC  ABC

Corr. s of  ∆s are  .

mDBC = mABC

Def. of  s.

mDBC  40.7°

Trans. Prop. of =


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

AB  DE

Check It Out! Example 2a

Given: ∆ABC  ∆DEF

Find the value of x.

Corr. sides of  ∆s are.

AB = DE

Def. of  parts.

Substitute values for AB and DE.

2x – 2 = 6

Add 2 to both sides.

2x = 8

x = 4

Divide both sides by 2.


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Check It Out! Example 2b

Given: ∆ABC  ∆DEF

Find mF.

∆ Sum Thm.

mEFD + mDEF + mFDE = 180°

ABC  DEF

Corr. s of  ∆are .

mABC = mDEF

Def. of  s.

mDEF = 53°

Transitive Prop. of =.

Substitute values for mDEF and mFDE.

mEFD + 53 + 90 = 180

mF + 143 = 180

Simplify.

mF = 37°

Subtract 143 from both sides.


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Given:YWXandYWZ are right angles.

YW bisects XYZ. W is the midpoint of XZ. XY  YZ.

Prove: ∆XYW  ∆ZYW

Example 3: Proving Triangles Congruent


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

5.W is mdpt. of XZ

6.XW ZW

7.YW YW

9.XY YZ

1.YWX and YWZ are rt. s.

1. Given

2.YWX  YWZ

2. Rt.   Thm.

3.YW bisects XYZ

3. Given

4.XYW  ZYW

4. Def. of bisector

5. Given

6. Def. of mdpt.

7. Reflex. Prop. of 

8.X  Z

8. Third s Thm.

9. Given

10.∆XYW  ∆ZYW

10. Def. of  ∆


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Check It Out! Example 3

Given:ADbisectsBE.

BEbisectsAD.

ABDE, A D

Prove:∆ABC  ∆DEC


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

4.ABDE

5.ADbisectsBE,

6.BC EC,

AC DC

BE bisects AD

1. A D

1. Given

2.BCA  DCE

2. Vertical s are .

3.ABC DEC

3. Third s Thm.

4. Given

5. Given

6. Def. of bisector

7.∆ABC  ∆DEC

7. Def. of  ∆s


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Example 4: Engineering Application

The diagonal bars across a gate give it support. Since the angle measures and the lengths of the corresponding sides are the same, the triangles are congruent.

Given: PR and QT bisect each other.

PQS  RTS, QP  RT

Prove: ∆QPS ∆TRS


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

1.QP RT

3.PR and QT bisect each other.

4.QS TS, PS  RS

Example 4 Continued

1. Given

2.PQS  RTS

2. Given

3. Given

4. Def. of bisector

5.QSP  TSR

5. Vert. s Thm.

6.QSP  TRS

6. Third s Thm.

7. ∆QPS  ∆TRS

7. Def. of  ∆s


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Given: MK bisects JL. JL bisects MK. JK ML.JK|| ML.

Check It Out! Example 4

Use the diagram to prove the following.

Prove: ∆JKN ∆LMN


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

2.JK|| ML

1.JK ML

4.JL and MK bisect each other.

5.JN LN, MN  KN

Check It Out! Example 4 Continued

1. Given

2. Given

3.JKN  NML

3. Alt int. s are .

4. Given

5. Def. of bisector

6.KNJ  MNL

6. Vert. s Thm.

7.KJN  MLN

7. Third s Thm.

8. ∆JKN ∆LMN

8. Def. of  ∆s


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

RS

Lesson Quiz

1. ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB.

Given that polygon MNOP polygon QRST, identify the congruent corresponding part.

2. NO  ____ 3. T  ____

4. Given: C is the midpoint of BD and AE.

A  E, AB  ED

Prove: ∆ABC  ∆EDC

31, 74

P


Warm up 1 name all sides and angles of fgh 2 what is true about k and l why

Statements

Reasons

1. A  E

1. Given

2. C is mdpt. of BD and AE

2. Given

3. AC EC; BC  DC

3. Def. of mdpt.

4. AB ED

4. Given

5. ACB  ECD

5. Vert. s Thm.

6. B  D

6. Third s Thm.

7. ABC  EDC

7. Def. of  ∆s

Lesson Quiz

4.


  • Login