HL Congruence.pptx

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Congruence Theorems — SSS — SAS

Triangle Congruence and HL

— ASA — AAS — HL

Hypotenuse – Leg Congruence Theorem

Right Triangles •  Congruence Theorem for right triangles

Hypotenuse •  The longest side •  Opposite from the 90° angle Legs •  The two sides that touch the 90° angle

SSA only works when the angle is 90° !!

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Example 1: Applying HL Congruence Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.

Example 2: Applying HL Congruence Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.

According to the diagram, the triangles are right triangles that share one leg. It is given that the hypotenuses are congruent, therefore the triangles are congruent by HL.

Example 3

Example 4 Identify the postulate or theorem that proves the triangles congruent.

Determine if you can use the HL Congruence Theorem to prove ΔABC ≅ ΔDCB. If not, tell what else you need to know. •  AC ≅ DB. (Hypotenuse) •  BC ≅ CB (Legs)

This conclusion cannot be proved by HL. According to the diagram, the triangles are right triangles and one pair of legs is congruent. You do not know that one hypotenuse is congruent to the other.

HL

ASA Given Reflexive Property

•  ∠ABC and ∠DCB are right angles Given •  ΔABC ≅ DCB

HL. SAS or SSS

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Example 5

Example 4

4. Given: ∠FAB ≅ ∠GED, ∠ABC ≅ ∠ DCE, AC ≅ EC Prove: ΔABC ≅ ΔEDC

Statements

Reasons

1. ∠FAB ≅ ∠GED

1. Given

2. ∠BAC is a supp. of ∠FAB; ∠DEC is a supp. of ∠GED.

2. Def. of supp. ∠s

3. ∠BAC ≅ ∠DEC

3. ≅ Supp. Thm.

4. ∠ACB ≅ ∠DCE; AC ≅ EC

4. Given

5. ΔABC ≅ ΔEDC

5. ASA (Steps 3,4)

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