Enumerate and explain the three (3) triangle congruence postulate?
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Enumerate and explain the three (3) triangle congruence postulate?
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Triangle Congruence Postulates
Five ways are available for finding two triangles congruent:
1. SSS, or Side Side Side
2. SAS, or Side Angle Side
3. ASA, or Angle Side Side
4. AAS, or Angle Angle Side
5. HL, or Hypotenuse Leg, for right triangles only
* Side Side Side Postulate
- A postulate is a statement taken to be true without proof. The SSS Postulate tells us,
- If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
* Side Angle Side Postulate
- The SAS Postulate tells us,
- If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
* Angle Side Angle Postulate
- This postulate says,
- If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
* Angle Angle Side Theorem
- We are given two angles and the non-included side, the side opposite one of the angles. The Angle Angle Side Theorem says,
- If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
* HL Postulate
- Exclusively for right triangles, the HL Postulate tells us,
- Two right triangles that have a congruent hypotenuse and a corresponding congruent leg are congruent.
Step-by-step explanation:
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