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Lesson 3.4: Proving Triangle Congruence by SAS, SSS, and HL
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Geometry

Lesson 3.4: Proving Triangle Congruence by SAS, SSS, and HL

Notes

SIDE-ANGLE-SIDE TRIANGLE CONGRUENCE NOTES

Side-Angle-Side (SAS) Congruence Postulate

  • If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
  • To use SAS Congruence, be sure that the congruent angle is formed by the congruent sides.
  • Said differently, the marked angle must be in between the marked sides.
  • Remember, Vertical Angles are also congruent and can be used to create the SAS Congruence.

EXAMPLE 1 - Name the included angle between the pair of sides given.

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EXAMPLE 2 –         State the third congruence that must be given to prove the triangles congruent using the SAS Congruence Theorem.

SIDE-SIDE-SIDE and HYPOTENUSE-LEG TRIANGLE CONGRUENCE NOTES

Side-Side-Side (SSS) Congruence Theorem

  • If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Hypotenuse-Leg (HL) Congruence Theorem

  • If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and corresponding leg of another triangle, then the two triangles are congruent.
  • This looks like SSA but it must use a right angle.

  • When triangles share a side, the Reflexive Property of Congruence provides another congruent pair of sides that can be used to create SSS or SAS or HL Congruence.

EXAMPLE 3  – Decide whether enough information is given to prove the triangles are congruent. If so, state the congruence postulate you would use.