Triangle Congruence Postulates

Triangle Congruence Postulates

Looking Back

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Consider $$\Delta DEF\cong\Delta GHI.$$ Let  $$m\angle D\ =\ 90^0$$  

         $$m\angle F=35^0,\ and$$               $$GI=3$$   Find the measure of $$\angle E$$ .

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Consider $$\Delta DEF\cong\Delta GHI.$$ Let  $$m\angle D\ =\ 90^0$$            $$m\angle F=35^0,\ and$$               $$GI=3$$   Find the measure of $$\angle H$$ .

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Consider $$\Delta DEF\cong\Delta GHI.$$
Let  $$m\angle D\ =\ 90^0$$  
         $$m\angle F=35^0,\ and$$
              $$GI=3$$  

Find the measure of $$\angle G$$ .

Fill in the Blank

Consider $$\Delta DEF\cong\Delta GHI.$$
Let  $$m\angle D\ =\ 90^0$$  
         $$m\angle F=35^0,\ and$$
              $$GI=3$$  

Find the measure of $$\angle I$$ .

Fill in the Blank

Consider $$\Delta DEF\cong\Delta GHI.$$
Let  $$m\angle D\ =\ 90^0$$  
         $$m\angle F=35^0,\ and$$
              $$GI=3$$  

Find the measure of $$DF$$ .

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Included Sides and Angles

Definitions

In a given triangle,

1. an angle is included by the sided of the triangle which are also sides of the angle;

2. a side is included by angles whose vertices are endpoints of the segments.

The Side-Angle-Side (SAS) Postulate

Let there be a correspondence between the vertices of two triangles.

If two sides and the included angle of one triangle are congruent to the corresponding parts of the second triangle, then the triangles are congruent.

The Angle-Side-Angle (ASA) Postulate

Let there be a correspondence between the vertices of two triangles.

If two angles and the included side of one triangle are congruent to the corresponding parts of the second triangle, then the triangles are congruent.

The Side-Side-Side (SSS) Postulate

Let there be a correspondence between the vertices of two triangles.

If three sides of one triangle are congruent to the corresponding three side of the second triangle, then the triangles are congruent.

The Angle-Angle-Side (AAS) Theorem

Let there be a correspondence between the vertices of two triangles.

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If two angles and the side opposite one of the angles in one triangle are congruent to the corresponding parts of the second triangle, then the two triangles are congruent.

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This theorem is sometimes called the Side-Angle-Angle (SAA) Theorem.

Try These!

State the postulate or theorem (SSS, SAS, ASA, or AAS) that can be used to conclude that the triangles are congruent.

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