Geometry a bellwork
Sponsored Links
This presentation is the property of its rightful owner.
1 / 17

Geometry A Bellwork PowerPoint PPT Presentation


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

Geometry A Bellwork. A. 3) Write a congruence statement that indicates that the two triangles are congruent. D. B. C. 4-4. Triangle Congruence: SSS and SAS. Holt Geometry. In Lesson 4-1, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent.

Download Presentation

Geometry A Bellwork

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


Geometry A Bellwork

A

3) Write a congruence statement that indicates that the two triangles are congruent.

D

B

C


4-4

Triangle Congruence: SSS and SAS

Holt Geometry


In Lesson 4-1, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent.

Now we will learn of several shortcuts to prove triangles congruent. We can prove them congruent using SIDE-SIDE-SIDE or SIDE-ANGLE-SIDE.


4-1


Remember!

Adjacent triangles share a side, so you can apply the Reflexive Property to get a pair of congruent parts.


It is given that AC DC and that AB  DB. By the Reflexive Property of Congruence, BC  BC. Therefore ∆ABC  ∆DBC by SSS.

Example 1: Using SSS to Prove Triangle Congruence

Use SSS to explain why ∆ABC  ∆DBC.


It is given that AB CD and BC  DA.

By the Reflexive Property of Congruence, AC  CA.

So ∆ABC  ∆CDA by SSS.

Check It Out! Example 1

Use SSS to explain why

∆ABC  ∆CDA.


An included angle is an angle formed by two adjacent sides of a polygon.

B is the included angle between sides AB and BC.


4-2


Caution

The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides.


It is given that BA BD and ABC  DBC. By the Reflexive Property of , BC  BC. So ∆ABC  ∆DBC by SAS.

Check It Out! Example 2

Use SAS to explain why ∆ABC  ∆DBC.


PQ  MN, QR  NO, PR  MO

Example 3A: Verifying Triangle Congruence

Determine if we know these triangles are congruent by SSS or SAS.

∆MNO  ∆PQR.

∆MNO  ∆PQR by SSS.


ST  VW, TU  WX, and T  W.

Example 3B: Verifying Triangle Congruence

Determine if we know these triangles are congruent by SSS or SAS.

∆STU  ∆VWX.

∆STU  ∆VWX by SAS.


Check It Out! Example 3

Determine if we know these triangles are congruent by SSS or SAS.

∆ADB  ∆CDB by SAS.


Example 4: Proving Triangles Congruent

Determine if we know these triangles are congruent by SSS or SAS.

∆ABD  ∆CDB

∆ABD  ∆CDB by SAS.


Lesson Quiz: Part I

Can SSS or SAS or none be used to prove the triangles congruent?

1.

none

2.

SSS


It is given that XZ VZ and that YZ  WZ. By the Vertical s Theorem. XZY  VZW. Therefore ∆XYZ  ∆VWZ by SAS.

Example 2: Engineering Application

The diagram shows part of the support structure for a tower. Use SAS to explain why ∆XYZ  ∆VWZ.


  • Login