Section 4.6 Hypotenuse-Leg

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Presentation transcript:

Section 4.6 Hypotenuse-Leg SWBAT: prove right triangles are congruent using the HL Theorem! Quick Review! X Y Z A B C leg leg hypotenuse leg hypotenuse leg

Hypotenuse-Leg (HL) Theorem: If the _______________ and one ______ of one RIGHT triangle are congruent to the hypotenuse and one leg of another ___________ triangle, then the triangles are congruent! hypotenuse leg right To use the HL Theorem, you must know/show: There are two right triangles The triangles have congruent hypotenuses There is one pair of corresponding congruent legs

Are the triangles congruent? If so, write the congruence statement. X Y Z A B C R S T U No; not rt triangles Yes by HL; ΔRUT  ΔSUT P O N M D E F L J Yes by AAS; ΔDEF  ΔJLF Yes by HL; ΔPOM  ΔMNP

Using the HL Theorem in PROOFS! Given: W J Z K Prove: Given 1. 1. ___________ Def of rt triangle 2. 2. ___________ 3. _______________ 3. Reflexive HL 4. 4. ___________