5.5 Proving Using SSS.

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Presentation transcript:

5.5 Proving Using SSS

What We Will Learn Use SSS (side-side-side) Thm Use HL (hypotenuse-leg) Thm

Needed Vocab Legs: sides adjacent to the right angle Hypotenuse: side opposite the right angle

Ex. 1 Using SSS Statement Reason 1. 𝐾𝐿 ≅ 𝑁𝐿 ; 𝐾𝑀 ≅ 𝑁𝑀 1. Given 1. 𝐾𝐿 ≅ 𝑁𝐿 ; 𝐾𝑀 ≅ 𝑁𝑀 1. Given 2. 𝐿𝑀 ≅ 𝐿𝑀 2. Reflex. Prop. 3. △𝐾𝐿𝑀≅△𝑁𝐿𝑀 3. SSS

Ex. 3 Using HL Thm Only with right triangles Soooooo… must say in proof they are right triangles Which means will have to say has a right angle if not said in given I separate triangles trying to prove and mark what I know Statement Reason 1. 𝑊𝑌 ≅ 𝑋𝑍 , 𝑊𝑍 ⊥ 𝑍𝑌 , 𝑋𝑌 ⊥ 𝑍𝑌 1. Given 2. ∠𝑍 𝑎𝑛𝑑 ∠𝑌 are right angles 2. Def. of perpendicular lines 3. △𝑊𝑌𝑍 𝑎𝑛𝑑 △𝑋𝑍𝑌 are right triangles 3. Def. of right triangles 4. 𝑍𝑌 ≅ 𝑍𝑌 4. Reflex. Prop. 5. △𝑊𝑌𝑍≅△𝑋𝑍𝑌 5. HL