Geometry a bellwork
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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.

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Geometry A Bellwork

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Geometry a bellwork

Geometry A Bellwork

A

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

D

B

C


Geometry a bellwork

4-4

Triangle Congruence: SSS and SAS

Holt Geometry


Geometry a bellwork

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.


Geometry a bellwork

4-1


Geometry a bellwork

Remember!

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


Geometry a bellwork

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.


Geometry a bellwork

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.


Geometry a bellwork

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

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


Geometry a bellwork

4-2


Geometry a bellwork

Caution

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


Geometry a bellwork

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.


Geometry a bellwork

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.


Geometry a bellwork

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.


Geometry a bellwork

Check It Out! Example 3

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

∆ADB  ∆CDB by SAS.


Geometry a bellwork

Example 4: Proving Triangles Congruent

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

∆ABD  ∆CDB

∆ABD  ∆CDB by SAS.


Geometry a bellwork

Lesson Quiz: Part I

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

1.

none

2.

SSS


Geometry a bellwork

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.


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