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Proving Triangles CongruentPowerPoint Presentation

Proving Triangles Congruent

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## PowerPoint Slideshow about ' Proving Triangles Congruent' - burian

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B

A

C

E

D

What does it mean for 2 triangles to be congruent?

Corresponding angles and sides should have the same measure.

- AB DE
- BC EF
- AC DF
- A D
- B E
- C F

B

A

C

E

F

D

If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

ABC DEF

And which ones?

What if we have all three angles?

- Use your protractor to draw Triangle ABC., so that:
- Angle A measures 70º,
- Angle B measures 30º and
- Angle C measures 80º.
- Now measure the lengths of the sides of your triangle.
- Compare your results with your partner. Are your triangles congruent?

No, the angles will be the same, but the triangles don’t have to be congruent.

Will 3 sides be enough for congruence?

- Make a triangle DEF so that:
- DE is 5 cm
- EF is 8 cm
- DF is 12 cm
- Now measure the angles. Compare your results with your partner. Are your triangles congruent?

SSS Congruence Conjecture

If the 3 sides of one triangle are congruent to the 3 sides of another triangle then the triangles are congruent.

SAS Congruence Conjecture

If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle then the triangles are congruent.

ASA Congruence Conjecture

If 2 angles and the included side of one triangle is congruent to two angles and the included side of another triangle, then the triangles are congruent.

AAS Congruence Conjecture

If 2 angles and a non-included side of one triangle is congruent to the corresponding angles and side of another triangle, then the triangles are included

- SSS correspondence
- ASA correspondence
- SAS correspondence
- AAS correspondence
- SSA correspondence
- AAA correspondence

The Congruence Postulates

(when possible)

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS

(when possible)

(when possible)

ACFE

Indicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

B D

For SAS:

AF

For AAS:

Indicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

For SAS:

For AAS:

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